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[poincare] Fix tests with Multiplication serialization (it always add

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the × operator
This commit is contained in:
Émilie Feral
2019-08-08 10:49:35 +02:00
parent d1ed886855
commit 081462ab5e
4 changed files with 286 additions and 286 deletions
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18
apps/calculation/test/calculation_store.cpp
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@@ -152,18 +152,18 @@ QUIZ_CASE(calculation_complex_format) {
assertCalculationDisplay("√(-1)", ::Calculation::Calculation::DisplayOutput::ApproximateOnly, ::Calculation::Calculation::EqualSign::Unknown, nullptr, "𝐢", &globalContext, &store);
assertCalculationDisplay("ln(-2)", ::Calculation::Calculation::DisplayOutput::ExactAndApproximate, ::Calculation::Calculation::EqualSign::Approximation, "ln(-2)", nullptr, &globalContext, &store);
assertCalculationDisplay("√(-1)×√(-1)", ::Calculation::Calculation::DisplayOutput::ApproximateOnly, ::Calculation::Calculation::EqualSign::Unknown, nullptr, "-1", &globalContext, &store);
assertCalculationDisplay("(-8)^(1/3)", ::Calculation::Calculation::DisplayOutput::ExactAndApproximate, ::Calculation::Calculation::EqualSign::Approximation, "1+√(3)𝐢", nullptr, &globalContext, &store);
assertCalculationDisplay("(-8)^(2/3)", ::Calculation::Calculation::DisplayOutput::ExactAndApproximate, ::Calculation::Calculation::EqualSign::Approximation, "-2+2√(3)𝐢", nullptr, &globalContext, &store);
assertCalculationDisplay("(-2)^(1/4)", ::Calculation::Calculation::DisplayOutput::ExactAndApproximate, ::Calculation::Calculation::EqualSign::Approximation, "root(8,4)/2+\u0012root(8,4)/2\u0013𝐢", nullptr, &globalContext, &store);
assertCalculationDisplay("(-8)^(1/3)", ::Calculation::Calculation::DisplayOutput::ExactAndApproximate, ::Calculation::Calculation::EqualSign::Approximation, "1+√(3)×𝐢", nullptr, &globalContext, &store);
assertCalculationDisplay("(-8)^(2/3)", ::Calculation::Calculation::DisplayOutput::ExactAndApproximate, ::Calculation::Calculation::EqualSign::Approximation, "-2+2×√(3)×𝐢", nullptr, &globalContext, &store);
assertCalculationDisplay("(-2)^(1/4)", ::Calculation::Calculation::DisplayOutput::ExactAndApproximate, ::Calculation::Calculation::EqualSign::Approximation, "root(8,4)/2+root(8,4)/2×𝐢", nullptr, &globalContext, &store);
Poincare::Preferences::sharedPreferences()->setComplexFormat(Poincare::Preferences::ComplexFormat::Polar);
assertCalculationDisplay("1+𝐢", ::Calculation::Calculation::DisplayOutput::ExactAndApproximate, ::Calculation::Calculation::EqualSign::Approximation, "√(2)ℯ^\u0012\u0012π/4\u0013𝐢\u0013", nullptr, &globalContext, &store);
assertCalculationDisplay("√(-1)", ::Calculation::Calculation::DisplayOutput::ExactAndApproximate, ::Calculation::Calculation::EqualSign::Approximation, "ℯ^\u0012\u0012π/2\u0013𝐢\u0013", nullptr, &globalContext, &store);
assertCalculationDisplay("1+𝐢", ::Calculation::Calculation::DisplayOutput::ExactAndApproximate, ::Calculation::Calculation::EqualSign::Approximation, "√(2)×ℯ^\u0012π/4×𝐢\u0013", nullptr, &globalContext, &store);
assertCalculationDisplay("√(-1)", ::Calculation::Calculation::DisplayOutput::ExactAndApproximate, ::Calculation::Calculation::EqualSign::Approximation, "ℯ^\u0012π/2×𝐢\u0013", nullptr, &globalContext, &store);
assertCalculationDisplay("ln(-2)", ::Calculation::Calculation::DisplayOutput::ExactAndApproximate, ::Calculation::Calculation::EqualSign::Approximation, "ln(-2)", nullptr, &globalContext, &store);
assertCalculationDisplay("√(-1)×√(-1)", ::Calculation::Calculation::DisplayOutput::ExactAndApproximate, ::Calculation::Calculation::EqualSign::Unknown, nullptr, "ℯ^\u00123.1415926535898𝐢\u0013", &globalContext, &store);
assertCalculationDisplay("(-8)^(1/3)", ::Calculation::Calculation::DisplayOutput::ExactAndApproximate, ::Calculation::Calculation::EqualSign::Approximation, "2ℯ^\u0012\u0012π/3\u0013𝐢\u0013", nullptr, &globalContext, &store);
assertCalculationDisplay("(-8)^(2/3)", ::Calculation::Calculation::DisplayOutput::ExactAndApproximate, ::Calculation::Calculation::EqualSign::Approximation, "4ℯ^\u0012\u00122π/3\u0013𝐢\u0013", nullptr, &globalContext, &store);
assertCalculationDisplay("(-2)^(1/4)", ::Calculation::Calculation::DisplayOutput::ExactAndApproximate, ::Calculation::Calculation::EqualSign::Approximation, "root(2,4)ℯ^\u0012\u0012π/4\u0013𝐢\u0013", nullptr, &globalContext, &store);
assertCalculationDisplay("√(-1)×√(-1)", ::Calculation::Calculation::DisplayOutput::ExactAndApproximate, ::Calculation::Calculation::EqualSign::Unknown, nullptr, "ℯ^\u00123.1415926535898×𝐢\u0013", &globalContext, &store);
assertCalculationDisplay("(-8)^(1/3)", ::Calculation::Calculation::DisplayOutput::ExactAndApproximate, ::Calculation::Calculation::EqualSign::Approximation, "2×ℯ^\u0012π/3×𝐢\u0013", nullptr, &globalContext, &store);
assertCalculationDisplay("(-8)^(2/3)", ::Calculation::Calculation::DisplayOutput::ExactAndApproximate, ::Calculation::Calculation::EqualSign::Approximation, "4×ℯ^\u0012\u00122×π\u0013/3×𝐢\u0013", nullptr, &globalContext, &store);
assertCalculationDisplay("(-2)^(1/4)", ::Calculation::Calculation::DisplayOutput::ExactAndApproximate, ::Calculation::Calculation::EqualSign::Approximation, "root(2,4)×ℯ^\u0012π/4×𝐢\u0013", nullptr, &globalContext, &store);
Poincare::Preferences::sharedPreferences()->setComplexFormat(Poincare::Preferences::ComplexFormat::Cartesian);
}

2
apps/solver/test/equation_store.cpp
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@@ -233,7 +233,7 @@ QUIZ_CASE(equation_solve_complex_format) {
assert_equation_system_exact_solve_to(equations1, EquationStore::Error::NoError, EquationStore::Type::LinearSystem, (const char **)variablesx, solutions0Polar, 1);
// x^2+x+1=0
const char * solutions2Polar[] = {"ℯ^\u0012-\u0012\u00122π\u0013/\u00123\u0013\u0013𝐢\u0013","ℯ^\u0012\u0012\u00122π\u0013/\u00123\u0013\u0013𝐢\u0013", "3ℯ^\u0012π𝐢\u0013"}; // ℯ^(-(2π/3)𝐢), ℯ^((2π/3)𝐢), 3ℯ^(π𝐢)
const char * solutions2Polar[] = {"ℯ^\u0012-\u0012\u00122π\u0013/\u00123\u0013\u0013𝐢\u0013","ℯ^\u0012\u0012\u00122π\u0013/\u00123\u0013\u0013𝐢\u0013", "3ℯ^\u0012π·𝐢\u0013"}; // ℯ^(-(2π/3)𝐢), ℯ^((2π/3)𝐢), 3ℯ^(π𝐢)
assert_equation_system_exact_solve_to(equations2, EquationStore::Error::NoError, EquationStore::Type::PolynomialMonovariable, (const char **)variablesx, solutions2Polar, 3);
// x^2-√(-1)=0

336
poincare/test/approximation.cpp
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@@ -91,14 +91,14 @@ QUIZ_CASE(poincare_approximation_infinity) {
QUIZ_CASE(poincare_approximation_addition) {
assert_expression_approximates_to<float>("1+2", "3");
assert_expression_approximates_to<float>("𝐢+𝐢", "2𝐢");
assert_expression_approximates_to<double>("2+𝐢+4+𝐢", "6+2𝐢");
assert_expression_approximates_to<float>("𝐢+𝐢", "2×𝐢");
assert_expression_approximates_to<double>("2+𝐢+4+𝐢", "6+2×𝐢");
assert_expression_approximates_to<float>("[[1,2][3,4][5,6]]+3", "undef");
assert_expression_approximates_to<double>("[[1,2+𝐢][3,4][5,6]]+3+𝐢", "undef");
assert_expression_approximates_to<float>("3+[[1,2][3,4][5,6]]", "undef");
assert_expression_approximates_to<double>("3+𝐢+[[1,2+𝐢][3,4][5,6]]", "undef");
assert_expression_approximates_to<float>("[[1,2][3,4][5,6]]+[[1,2][3,4][5,6]]", "[[2,4][6,8][10,12]]");
assert_expression_approximates_to<double>("[[1,2+𝐢][3,4][5,6]]+[[1,2+𝐢][3,4][5,6]]", "[[2,4+2𝐢][6,8][10,12]]");
assert_expression_approximates_to<double>("[[1,2+𝐢][3,4][5,6]]+[[1,2+𝐢][3,4][5,6]]", "[[2,4+2×𝐢][6,8][10,12]]");
assert_expression_approximates_to_scalar<float>("1+2", 3.0f);
assert_expression_approximates_to_scalar<double>("𝐢+𝐢", NAN);
@@ -107,13 +107,13 @@ QUIZ_CASE(poincare_approximation_addition) {
QUIZ_CASE(poincare_approximation_multiplication) {
assert_expression_approximates_to<float>("1×2", "2");
assert_expression_approximates_to<double>("(3+𝐢)×(4+𝐢)", "11+7𝐢");
assert_expression_approximates_to<double>("(3+𝐢)×(4+𝐢)", "11+7×𝐢");
assert_expression_approximates_to<float>("[[1,2][3,4][5,6]]×2", "[[2,4][6,8][10,12]]");
assert_expression_approximates_to<double>("[[1,2+𝐢][3,4][5,6]]×(3+𝐢)", "[[3+𝐢,5+5𝐢][9+3𝐢,12+4𝐢][15+5𝐢,18+6𝐢]]");
assert_expression_approximates_to<double>("[[1,2+𝐢][3,4][5,6]]×(3+𝐢)", "[[3+𝐢,5+5×𝐢][9+3×𝐢,12+4×𝐢][15+5×𝐢,18+6×𝐢]]");
assert_expression_approximates_to<float>("2×[[1,2][3,4][5,6]]", "[[2,4][6,8][10,12]]");
assert_expression_approximates_to<double>("(3+𝐢)×[[1,2+𝐢][3,4][5,6]]", "[[3+𝐢,5+5𝐢][9+3𝐢,12+4𝐢][15+5𝐢,18+6𝐢]]");
assert_expression_approximates_to<double>("(3+𝐢)×[[1,2+𝐢][3,4][5,6]]", "[[3+𝐢,5+5×𝐢][9+3×𝐢,12+4×𝐢][15+5×𝐢,18+6×𝐢]]");
assert_expression_approximates_to<float>("[[1,2][3,4][5,6]]×[[1,2,3,4][5,6,7,8]]", "[[11,14,17,20][23,30,37,44][35,46,57,68]]");
assert_expression_approximates_to<double>("[[1,2+𝐢][3,4][5,6]]×[[1,2+𝐢,3,4][5,6+𝐢,7,8]]", "[[11+5𝐢,13+9𝐢,17+7𝐢,20+8𝐢][23,30+7𝐢,37,44][35,46+11𝐢,57,68]]");
assert_expression_approximates_to<double>("[[1,2+𝐢][3,4][5,6]]×[[1,2+𝐢,3,4][5,6+𝐢,7,8]]", "[[11+5×𝐢,13+9×𝐢,17+7×𝐢,20+8×𝐢][23,30+7×𝐢,37,44][35,46+11×𝐢,57,68]]");
assert_expression_approximates_to_scalar<float>("1×2", 2.0f);
assert_expression_approximates_to_scalar<double>("(3+𝐢)×(4+𝐢)", NAN);
@@ -122,15 +122,15 @@ QUIZ_CASE(poincare_approximation_multiplication) {
QUIZ_CASE(poincare_approximation_power) {
assert_expression_approximates_to<float>("2^3", "8");
assert_expression_approximates_to<double>("(3+𝐢)^4", "28+96𝐢");
assert_expression_approximates_to<float>("4^(3+𝐢)", "11.74125+62.91378𝐢");
assert_expression_approximates_to<double>("(3+𝐢)^(3+𝐢)", "-11.898191759852+19.592921596609𝐢");
assert_expression_approximates_to<double>("(3+𝐢)^4", "28+96×𝐢");
assert_expression_approximates_to<float>("4^(3+𝐢)", "11.74125+62.91378×𝐢");
assert_expression_approximates_to<double>("(3+𝐢)^(3+𝐢)", "-11.898191759852+19.592921596609×𝐢");
assert_expression_approximates_to<double>("0^0", Undefined::Name());
assert_expression_approximates_to<double>("0^2", "0");
assert_expression_approximates_to<double>("0^(-2)", Undefined::Name());
assert_expression_approximates_to<double>("(-2)^4.2", "14.8690638497+10.8030072384𝐢", Radian, Cartesian, 12);
assert_expression_approximates_to<double>("(-2)^4.2", "14.8690638497+10.8030072384×𝐢", Radian, Cartesian, 12);
assert_expression_approximates_to<double>("(-0.1)^4", "0.0001", Radian, Cartesian, 12);
assert_expression_approximates_to<float>("0^2", "0");
@@ -141,12 +141,12 @@ QUIZ_CASE(poincare_approximation_power) {
assert_expression_approximates_to<double>("ℯ^(𝐢×π)", "-1");
assert_expression_approximates_to<float>("ℯ^(𝐢×π+2)", "-7.38906", Radian, Cartesian, 6);
assert_expression_approximates_to<double>("ℯ^(𝐢×π+2)", "-7.3890560989307");
assert_expression_approximates_to<float>("(-1)^(1/3)", "0.5+0.8660254𝐢");
assert_expression_approximates_to<double>("(-1)^(1/3)", "0.5+8.6602540378444ᴇ-1𝐢");
assert_expression_approximates_to<float>("ℯ^(𝐢×π/3)", "0.5+0.866025𝐢", Radian, Cartesian, 6);
assert_expression_approximates_to<double>("ℯ^(𝐢×π/3)", "0.5+8.6602540378444ᴇ-1𝐢");
assert_expression_approximates_to<float>("𝐢^(2/3)", "0.5+0.8660254𝐢");
assert_expression_approximates_to<double>("𝐢^(2/3)", "0.5+8.6602540378444ᴇ-1𝐢");
assert_expression_approximates_to<float>("(-1)^(1/3)", "0.5+0.8660254×𝐢");
assert_expression_approximates_to<double>("(-1)^(1/3)", "0.5+8.6602540378444ᴇ-1×𝐢");
assert_expression_approximates_to<float>("ℯ^(𝐢×π/3)", "0.5+0.866025×𝐢", Radian, Cartesian, 6);
assert_expression_approximates_to<double>("ℯ^(𝐢×π/3)", "0.5+8.6602540378444ᴇ-1×𝐢");
assert_expression_approximates_to<float>("𝐢^(2/3)", "0.5+0.8660254×𝐢");
assert_expression_approximates_to<double>("𝐢^(2/3)", "0.5+8.6602540378444ᴇ-1×𝐢");
assert_expression_approximates_to_scalar<float>("2^3", 8.0f);
assert_expression_approximates_to_scalar<double>("(3+𝐢)^(4+𝐢)", NAN);
@@ -180,15 +180,15 @@ QUIZ_CASE(poincare_approximation_constant) {
QUIZ_CASE(poincare_approximation_division) {
assert_expression_approximates_to<float>("1/2", "0.5");
assert_expression_approximates_to<double>("(3+𝐢)/(4+𝐢)", "7.6470588235294ᴇ-1+5.8823529411765ᴇ-2𝐢");
assert_expression_approximates_to<double>("(3+𝐢)/(4+𝐢)", "7.6470588235294ᴇ-1+5.8823529411765ᴇ-2×𝐢");
assert_expression_approximates_to<float>("[[1,2][3,4][5,6]]/2", "[[0.5,1][1.5,2][2.5,3]]");
assert_expression_approximates_to<double>("[[1,2+𝐢][3,4][5,6]]/(1+𝐢)", "[[0.5-0.5𝐢,1.5-0.5𝐢][1.5-1.5𝐢,2-2𝐢][2.5-2.5𝐢,3-3𝐢]]");
assert_expression_approximates_to<double>("[[1,2+𝐢][3,4][5,6]]/(1+𝐢)", "[[0.5-0.5×𝐢,1.5-0.5×𝐢][1.5-1.5×𝐢,2-2×𝐢][2.5-2.5×𝐢,3-3×𝐢]]");
assert_expression_approximates_to<float>("[[1,2][3,4][5,6]]/2", "[[0.5,1][1.5,2][2.5,3]]");
assert_expression_approximates_to<double>("[[1,2][3,4]]/[[3,4][6,9]]", "[[-1,6.6666666666667ᴇ-1][1,0]]");
assert_expression_approximates_to<double>("3/[[3,4][5,6]]", "[[-9,6][7.5,-4.5]]");
assert_expression_approximates_to<double>("(3+4𝐢)/[[1,𝐢][3,4]]", "[[4𝐢,1][-3𝐢,𝐢]]");
assert_expression_approximates_to<float>("1ᴇ20/(1ᴇ20+1ᴇ20𝐢)", "0.5-0.5𝐢");
assert_expression_approximates_to<double>("1ᴇ155/(1ᴇ155+1ᴇ155𝐢)", "0.5-0.5𝐢");
assert_expression_approximates_to<double>("(3+4𝐢)/[[1,𝐢][3,4]]", "[[4×𝐢,1][-3×𝐢,𝐢]]");
assert_expression_approximates_to<float>("1ᴇ20/(1ᴇ20+1ᴇ20𝐢)", "0.5-0.5×𝐢");
assert_expression_approximates_to<double>("1ᴇ155/(1ᴇ155+1ᴇ155𝐢)", "0.5-0.5×𝐢");
assert_expression_approximates_to_scalar<float>("1/2", 0.5f);
assert_expression_approximates_to_scalar<float>("(3+𝐢)/(4+𝐢)", NAN);
@@ -200,16 +200,16 @@ QUIZ_CASE(poincare_approximation_logarithm) {
assert_expression_approximates_to<double>("log(6,7)", "0.9207822211616");
assert_expression_approximates_to<float>("log(5)", "0.69897");
assert_expression_approximates_to<double>("ln(5)", "1.6094379124341");
assert_expression_approximates_to<float>("log(2+5×𝐢,64)", "0.4048317+0.2862042𝐢");
assert_expression_approximates_to<double>("log(6,7+4×𝐢)", "8.0843880717528ᴇ-1-2.0108238082167ᴇ-1𝐢");
assert_expression_approximates_to<float>("log(5+2×𝐢)", "0.731199+0.1652518𝐢");
assert_expression_approximates_to<double>("ln(5+2×𝐢)", "1.6836479149932+3.8050637711236ᴇ-1𝐢");
assert_expression_approximates_to<float>("log(2+5×𝐢,64)", "0.4048317+0.2862042×𝐢");
assert_expression_approximates_to<double>("log(6,7+4×𝐢)", "8.0843880717528ᴇ-1-2.0108238082167ᴇ-1×𝐢");
assert_expression_approximates_to<float>("log(5+2×𝐢)", "0.731199+0.1652518×𝐢");
assert_expression_approximates_to<double>("ln(5+2×𝐢)", "1.6836479149932+3.8050637711236ᴇ-1×𝐢");
assert_expression_approximates_to<double>("log(0,0)", Undefined::Name());
assert_expression_approximates_to<double>("log(0)", "-inf");
assert_expression_approximates_to<double>("log(2,0)", "0");
// WARNING: evaluate on branch cut can be multivalued
assert_expression_approximates_to<double>("ln(-4)", "1.3862943611199+3.1415926535898𝐢");
assert_expression_approximates_to<double>("ln(-4)", "1.3862943611199+3.1415926535898×𝐢");
}
template<typename T>
@@ -243,8 +243,8 @@ QUIZ_CASE(poincare_approximation_function) {
assert_expression_approximates_to<float>("det([[1,23,3][4,5,6][7,8,9]])", "126", Degree, Cartesian, 6); // FIXME: the determinant computation is not precised enough to be displayed with 7 significant digits
assert_expression_approximates_to<double>("det([[1,23,3][4,5,6][7,8,9]])", "126");
assert_expression_approximates_to<float>("det([[𝐢,23-2𝐢,3×𝐢][4+𝐢,5×𝐢,6][7,8×𝐢+2,9]])", "126-231𝐢", Degree, Cartesian, 6); // FIXME: the determinant computation is not precised enough to be displayed with 7 significant digits
assert_expression_approximates_to<double>("det([[𝐢,23-2𝐢,3×𝐢][4+𝐢,5×𝐢,6][7,8×𝐢+2,9]])", "126-231𝐢");
assert_expression_approximates_to<float>("det([[𝐢,23-2𝐢,3×𝐢][4+𝐢,5×𝐢,6][7,8×𝐢+2,9]])", "126-231×𝐢", Degree, Cartesian, 6); // FIXME: the determinant computation is not precised enough to be displayed with 7 significant digits
assert_expression_approximates_to<double>("det([[𝐢,23-2𝐢,3×𝐢][4+𝐢,5×𝐢,6][7,8×𝐢+2,9]])", "126-231×𝐢");
assert_expression_approximates_to<float>("diff(2×x, x, 2)", "2");
assert_expression_approximates_to<double>("diff(2×x, x, 2)", "2");
@@ -311,16 +311,16 @@ QUIZ_CASE(poincare_approximation_function) {
assert_expression_approximates_to<float>("dim([[1,2,3][4,5,-6]])", "[[2,3]]");
assert_expression_approximates_to<double>("dim([[1,2,3][4,5,-6]])", "[[2,3]]");
assert_expression_approximates_to<float>("conj(3+2×𝐢)", "3-2𝐢");
assert_expression_approximates_to<double>("conj(3+2×𝐢)", "3-2𝐢");
assert_expression_approximates_to<float>("conj(3+2×𝐢)", "3-2×𝐢");
assert_expression_approximates_to<double>("conj(3+2×𝐢)", "3-2×𝐢");
assert_expression_approximates_to<float>("factor(-23/4)", "-5.75");
assert_expression_approximates_to<double>("factor(-123/24)", "-5.125");
assert_expression_approximates_to<float>("inverse([[1,2,3][4,5,-6][7,8,9]])", "[[-1.2917,-0.083333,0.375][1.0833,0.16667,-0.25][0.041667,-0.083333,0.041667]]", Degree, Cartesian, 5); // inverse is not precise enough to display 7 significative digits
assert_expression_approximates_to<double>("inverse([[1,2,3][4,5,-6][7,8,9]])", "[[-1.2916666666667,-8.3333333333333ᴇ-2,0.375][1.0833333333333,1.6666666666667ᴇ-1,-0.25][4.1666666666667ᴇ-2,-8.3333333333333ᴇ-2,4.1666666666667ᴇ-2]]");
assert_expression_approximates_to<float>("inverse([[𝐢,23-2𝐢,3×𝐢][4+𝐢,5×𝐢,6][7,8×𝐢+2,9]])", "[[-0.0118-0.0455𝐢,-0.5-0.727𝐢,0.318+0.489𝐢][0.0409+0.00364𝐢,0.04-0.0218𝐢,-0.0255+0.00091𝐢][0.00334-0.00182𝐢,0.361+0.535𝐢,-0.13-0.358𝐢]]", Degree, Cartesian, 3); // inverse is not precise enough to display 7 significative digits
assert_expression_approximates_to<double>("inverse([[𝐢,23-2𝐢,3×𝐢][4+𝐢,5×𝐢,6][7,8×𝐢+2,9]])", "[[-0.0118289353958-0.0454959053685𝐢,-0.500454959054-0.727024567789𝐢,0.31847133758+0.488626023658𝐢][0.0409463148317+3.63967242948ᴇ-3𝐢,0.0400363967243-0.0218380345769𝐢,-0.0254777070064+9.0991810737ᴇ-4𝐢][3.33636639369ᴇ-3-1.81983621474ᴇ-3𝐢,0.36093418259+0.534728541098𝐢,-0.130118289354-0.357597816197𝐢]]", Degree, Cartesian, 12); // FIXME: inverse is not precise enough to display 14 significative digits
assert_expression_approximates_to<float>("inverse([[𝐢,23-2𝐢,3×𝐢][4+𝐢,5×𝐢,6][7,8×𝐢+2,9]])", "[[-0.0118-0.0455×𝐢,-0.5-0.727×𝐢,0.318+0.489×𝐢][0.0409+0.00364×𝐢,0.04-0.0218×𝐢,-0.0255+0.00091×𝐢][0.00334-0.00182×𝐢,0.361+0.535×𝐢,-0.13-0.358×𝐢]]", Degree, Cartesian, 3); // inverse is not precise enough to display 7 significative digits
assert_expression_approximates_to<double>("inverse([[𝐢,23-2𝐢,3×𝐢][4+𝐢,5×𝐢,6][7,8×𝐢+2,9]])", "[[-0.0118289353958-0.0454959053685×𝐢,-0.500454959054-0.727024567789×𝐢,0.31847133758+0.488626023658×𝐢][0.0409463148317+3.63967242948ᴇ-3×𝐢,0.0400363967243-0.0218380345769×𝐢,-0.0254777070064+9.0991810737ᴇ-4×𝐢][3.33636639369ᴇ-3-1.81983621474ᴇ-3×𝐢,0.36093418259+0.534728541098×𝐢,-0.130118289354-0.357597816197×𝐢]]", Degree, Cartesian, 12); // FIXME: inverse is not precise enough to display 14 significative digits
assert_expression_approximates_to<float>("prediction(0.1, 100)", "[[0,0.2]]");
assert_expression_approximates_to<double>("prediction(0.1, 100)", "[[0,0.2]]");
@@ -328,20 +328,20 @@ QUIZ_CASE(poincare_approximation_function) {
assert_expression_approximates_to<float>("prediction95(0.1, 100)", "[[0.0412,0.1588]]");
assert_expression_approximates_to<double>("prediction95(0.1, 100)", "[[0.0412,0.1588]]");
assert_expression_approximates_to<float>("product(2+k×𝐢,k, 1, 5)", "-100-540𝐢");
assert_expression_approximates_to<double>("product(2+o×𝐢,o, 1, 5)", "-100-540𝐢");
assert_expression_approximates_to<float>("product(2+k×𝐢,k, 1, 5)", "-100-540×𝐢");
assert_expression_approximates_to<double>("product(2+o×𝐢,o, 1, 5)", "-100-540×𝐢");
assert_expression_approximates_to<float>("root(3+𝐢, 3)", "1.459366+0.1571201𝐢");
assert_expression_approximates_to<double>("root(3+𝐢, 3)", "1.4593656008684+1.5712012294394ᴇ-1𝐢");
assert_expression_approximates_to<float>("root(3+𝐢, 3)", "1.459366+0.1571201×𝐢");
assert_expression_approximates_to<double>("root(3+𝐢, 3)", "1.4593656008684+1.5712012294394ᴇ-1×𝐢");
assert_expression_approximates_to<float>("root(3, 3+𝐢)", "1.382007-0.1524428𝐢");
assert_expression_approximates_to<double>("root(3, 3+𝐢)", "1.3820069623326-0.1524427794159𝐢");
assert_expression_approximates_to<float>("root(3, 3+𝐢)", "1.382007-0.1524428×𝐢");
assert_expression_approximates_to<double>("root(3, 3+𝐢)", "1.3820069623326-0.1524427794159×𝐢");
assert_expression_approximates_to<float>("root(5^((-𝐢)3^9),𝐢)", "3.504", Degree, Cartesian, 4);
assert_expression_approximates_to<double>("root(5^((-𝐢)3^9),𝐢)", "3.5039410843", Degree, Cartesian, 11);
assert_expression_approximates_to<float>("√(3+𝐢)", "1.755317+0.2848488𝐢");
assert_expression_approximates_to<double>("√(3+𝐢)", "1.7553173018244+2.8484878459314ᴇ-1𝐢");
assert_expression_approximates_to<float>("√(3+𝐢)", "1.755317+0.2848488×𝐢");
assert_expression_approximates_to<double>("√(3+𝐢)", "1.7553173018244+2.8484878459314ᴇ-1×𝐢");
assert_expression_approximates_to<float>("sign(-23+1)", "-1");
assert_expression_approximates_to<float>("sign(inf)", "1");
@@ -352,8 +352,8 @@ QUIZ_CASE(poincare_approximation_function) {
assert_expression_approximates_to<double>("sign(2+𝐢)", "undef");
assert_expression_approximates_to<double>("sign(undef)", "undef");
assert_expression_approximates_to<double>("sum(2+n×𝐢,n,1,5)", "10+15𝐢");
assert_expression_approximates_to<double>("sum(2+n×𝐢,n,1,5)", "10+15𝐢");
assert_expression_approximates_to<double>("sum(2+n×𝐢,n,1,5)", "10+15×𝐢");
assert_expression_approximates_to<double>("sum(2+n×𝐢,n,1,5)", "10+15×𝐢");
assert_expression_approximates_to<float>("transpose([[1,2,3][4,5,-6][7,8,9]])", "[[1,4,7][2,5,8][3,-6,9]]");
assert_expression_approximates_to<float>("transpose([[1,7,5][4,2,8]])", "[[1,4][7,2][5,8]]");
@@ -371,8 +371,8 @@ QUIZ_CASE(poincare_approximation_function) {
assert_expression_approximates_to<float>("√(-1)", "𝐢");
assert_expression_approximates_to<double>("√(-1)", "𝐢");
assert_expression_approximates_to<float>("root(-1,3)", "0.5+0.8660254𝐢");
assert_expression_approximates_to<double>("root(-1,3)", "0.5+8.6602540378444ᴇ-1𝐢");
assert_expression_approximates_to<float>("root(-1,3)", "0.5+0.8660254×𝐢");
assert_expression_approximates_to<double>("root(-1,3)", "0.5+8.6602540378444ᴇ-1×𝐢");
assert_expression_approximates_to<float>("int(int(x×x,x,0,x),x,0,4)", "21.33333");
assert_expression_approximates_to<double>("int(int(x×x,x,0,x),x,0,4)", "21.333333333333");
@@ -406,8 +406,8 @@ QUIZ_CASE(poincare_approximation_trigonometry_functions) {
assert_expression_approximates_to<double>("cos(2×𝐢)", "3.7621956910836", Radian);
assert_expression_approximates_to<double>("cos(2×𝐢)", "1.0006092967033", Degree);
// On C
assert_expression_approximates_to<float>("cos(𝐢-4)", "-1.008625-0.8893952𝐢", Radian);
assert_expression_approximates_to<float>("cos(𝐢-4)", "0.997716+0.00121754𝐢", Degree, Cartesian, 6);
assert_expression_approximates_to<float>("cos(𝐢-4)", "-1.008625-0.8893952×𝐢", Radian);
assert_expression_approximates_to<float>("cos(𝐢-4)", "0.997716+0.00121754×𝐢", Degree, Cartesian, 6);
/* sin: R -> R (oscillator)
* Ri -> Ri (odd)
@@ -421,14 +421,14 @@ QUIZ_CASE(poincare_approximation_trigonometry_functions) {
assert_expression_approximates_to<float>("sin(3×π)", "0", Radian);
assert_expression_approximates_to<float>("sin(-540)", "0", Degree);
// On R×i
assert_expression_approximates_to<double>("sin(3×𝐢)", "10.01787492741𝐢", Radian);
assert_expression_approximates_to<float>("sin(3×𝐢)", "0.05238381𝐢", Degree);
assert_expression_approximates_to<double>("sin(3×𝐢)", "10.01787492741×𝐢", Radian);
assert_expression_approximates_to<float>("sin(3×𝐢)", "0.05238381×𝐢", Degree);
// Symmetry: odd
assert_expression_approximates_to<double>("sin(-3×𝐢)", "-10.01787492741𝐢", Radian);
assert_expression_approximates_to<float>("sin(-3×𝐢)", "-0.05238381𝐢", Degree);
assert_expression_approximates_to<double>("sin(-3×𝐢)", "-10.01787492741×𝐢", Radian);
assert_expression_approximates_to<float>("sin(-3×𝐢)", "-0.05238381×𝐢", Degree);
// On: C
assert_expression_approximates_to<float>("sin(𝐢-4)", "1.16781-0.768163𝐢", Radian, Cartesian, 6);
assert_expression_approximates_to<float>("sin(𝐢-4)", "-0.0697671+0.0174117𝐢", Degree, Cartesian, 6);
assert_expression_approximates_to<float>("sin(𝐢-4)", "1.16781-0.768163×𝐢", Radian, Cartesian, 6);
assert_expression_approximates_to<float>("sin(𝐢-4)", "-0.0697671+0.0174117×𝐢", Degree, Cartesian, 6);
assert_expression_approximates_to<float>("sin(1.234567890123456ᴇ-15)", "1.23457ᴇ-15", Radian, Cartesian, 6);
/* tan: R -> R (tangent-style)
@@ -443,14 +443,14 @@ QUIZ_CASE(poincare_approximation_trigonometry_functions) {
assert_expression_approximates_to<float>("tan(3×π)", "0", Radian);
assert_expression_approximates_to<float>("tan(-540)", "0", Degree);
// On R×i
assert_expression_approximates_to<double>("tan(-2×𝐢)", "-9.6402758007582ᴇ-1𝐢", Radian);
assert_expression_approximates_to<float>("tan(-2×𝐢)", "-0.03489241𝐢", Degree);
assert_expression_approximates_to<double>("tan(-2×𝐢)", "-9.6402758007582ᴇ-1×𝐢", Radian);
assert_expression_approximates_to<float>("tan(-2×𝐢)", "-0.03489241×𝐢", Degree);
// Symmetry: odd
assert_expression_approximates_to<double>("tan(2×𝐢)", "9.6402758007582ᴇ-1𝐢", Radian);
assert_expression_approximates_to<float>("tan(2×𝐢)", "0.03489241𝐢", Degree);
assert_expression_approximates_to<double>("tan(2×𝐢)", "9.6402758007582ᴇ-1×𝐢", Radian);
assert_expression_approximates_to<float>("tan(2×𝐢)", "0.03489241×𝐢", Degree);
// On C
assert_expression_approximates_to<float>("tan(𝐢-4)", "-0.273553+1.00281𝐢", Radian, Cartesian, 6);
assert_expression_approximates_to<float>("tan(𝐢-4)", "-0.0699054+0.0175368𝐢", Degree, Cartesian, 6);
assert_expression_approximates_to<float>("tan(𝐢-4)", "-0.273553+1.00281×𝐢", Radian, Cartesian, 6);
assert_expression_approximates_to<float>("tan(𝐢-4)", "-0.0699054+0.0175368×𝐢", Degree, Cartesian, 6);
/* acos: [-1,1] -> R
* ]-inf,-1[ -> π+R×i (odd imaginary)
@@ -462,23 +462,23 @@ QUIZ_CASE(poincare_approximation_trigonometry_functions) {
assert_expression_approximates_to<double>("acos(0.03)", "1.5407918249714", Radian);
assert_expression_approximates_to<double>("acos(0.5)", "60", Degree);
// On [1, inf[
assert_expression_approximates_to<double>("acos(2)", "1.3169578969248𝐢", Radian);
assert_expression_approximates_to<double>("acos(2)", "75.456129290217𝐢", Degree);
assert_expression_approximates_to<double>("acos(2)", "1.3169578969248×𝐢", Radian);
assert_expression_approximates_to<double>("acos(2)", "75.456129290217×𝐢", Degree);
// Symmetry: odd on imaginary
assert_expression_approximates_to<double>("acos(-2)", "3.1415926535898-1.3169578969248𝐢", Radian);
assert_expression_approximates_to<double>("acos(-2)", "180-75.456129290217𝐢", Degree);
assert_expression_approximates_to<double>("acos(-2)", "3.1415926535898-1.3169578969248×𝐢", Radian);
assert_expression_approximates_to<double>("acos(-2)", "180-75.456129290217×𝐢", Degree);
// On ]-inf, -1[
assert_expression_approximates_to<double>("acos(-32)", "3.14159265359-4.158638853279𝐢", Radian, Cartesian, 13);
assert_expression_approximates_to<float>("acos(-32)", "180-238.3𝐢", Degree, Cartesian, 4);
assert_expression_approximates_to<double>("acos(-32)", "3.14159265359-4.158638853279×𝐢", Radian, Cartesian, 13);
assert_expression_approximates_to<float>("acos(-32)", "180-238.3×𝐢", Degree, Cartesian, 4);
// On R×i
assert_expression_approximates_to<float>("acos(3×𝐢)", "1.5708-1.8184𝐢", Radian, Cartesian, 5);
assert_expression_approximates_to<float>("acos(3×𝐢)", "90-104.19𝐢", Degree, Cartesian, 5);
assert_expression_approximates_to<float>("acos(3×𝐢)", "1.5708-1.8184×𝐢", Radian, Cartesian, 5);
assert_expression_approximates_to<float>("acos(3×𝐢)", "90-104.19×𝐢", Degree, Cartesian, 5);
// Symmetry: odd on imaginary
assert_expression_approximates_to<float>("acos(-3×𝐢)", "1.5708+1.8184𝐢", Radian, Cartesian, 5);
assert_expression_approximates_to<float>("acos(-3×𝐢)", "90+104.19𝐢", Degree, Cartesian, 5);
assert_expression_approximates_to<float>("acos(-3×𝐢)", "1.5708+1.8184×𝐢", Radian, Cartesian, 5);
assert_expression_approximates_to<float>("acos(-3×𝐢)", "90+104.19×𝐢", Degree, Cartesian, 5);
// On C
assert_expression_approximates_to<float>("acos(𝐢-4)", "2.8894-2.0966𝐢", Radian, Cartesian, 5);
assert_expression_approximates_to<float>("acos(𝐢-4)", "165.551-120.126𝐢", Degree, Cartesian, 6);
assert_expression_approximates_to<float>("acos(𝐢-4)", "2.8894-2.0966×𝐢", Radian, Cartesian, 5);
assert_expression_approximates_to<float>("acos(𝐢-4)", "165.551-120.126×𝐢", Degree, Cartesian, 6);
// Key values
assert_expression_approximates_to<double>("acos(0)", "90", Degree);
assert_expression_approximates_to<float>("acos(-1)", "180", Degree);
@@ -494,21 +494,21 @@ QUIZ_CASE(poincare_approximation_trigonometry_functions) {
assert_expression_approximates_to<double>("asin(0.03)", "3.0004501823477ᴇ-2", Radian);
assert_expression_approximates_to<double>("asin(0.5)", "30", Degree);
// On [1, inf[
assert_expression_approximates_to<double>("asin(2)", "1.5707963267949-1.3169578969248𝐢", Radian);
assert_expression_approximates_to<double>("asin(2)", "90-75.456129290217𝐢", Degree);
assert_expression_approximates_to<double>("asin(2)", "1.5707963267949-1.3169578969248×𝐢", Radian);
assert_expression_approximates_to<double>("asin(2)", "90-75.456129290217×𝐢", Degree);
// Symmetry: odd
assert_expression_approximates_to<double>("asin(-2)", "-1.5707963267949+1.3169578969248𝐢", Radian);
assert_expression_approximates_to<double>("asin(-2)", "-90+75.456129290217𝐢", Degree);
assert_expression_approximates_to<double>("asin(-2)", "-1.5707963267949+1.3169578969248×𝐢", Radian);
assert_expression_approximates_to<double>("asin(-2)", "-90+75.456129290217×𝐢", Degree);
// On ]-inf, -1[
assert_expression_approximates_to<float>("asin(-32)", "-1.571+4.159𝐢", Radian, Cartesian, 4);
assert_expression_approximates_to<float>("asin(-32)", "-90+238𝐢", Degree, Cartesian, 3);
assert_expression_approximates_to<float>("asin(-32)", "-1.571+4.159×𝐢", Radian, Cartesian, 4);
assert_expression_approximates_to<float>("asin(-32)", "-90+238×𝐢", Degree, Cartesian, 3);
// On R×i
assert_expression_approximates_to<double>("asin(3×𝐢)", "1.8184464592321𝐢", Radian);
assert_expression_approximates_to<double>("asin(3×𝐢)", "1.8184464592321×𝐢", Radian);
// Symmetry: odd
assert_expression_approximates_to<double>("asin(-3×𝐢)", "-1.8184464592321𝐢", Radian);
assert_expression_approximates_to<double>("asin(-3×𝐢)", "-1.8184464592321×𝐢", Radian);
// On C
assert_expression_approximates_to<float>("asin(𝐢-4)", "-1.3186+2.0966𝐢", Radian, Cartesian, 5);
assert_expression_approximates_to<float>("asin(𝐢-4)", "-75.551+120.13𝐢", Degree, Cartesian, 5);
assert_expression_approximates_to<float>("asin(𝐢-4)", "-1.3186+2.0966×𝐢", Radian, Cartesian, 5);
assert_expression_approximates_to<float>("asin(𝐢-4)", "-75.551+120.13×𝐢", Degree, Cartesian, 5);
// Key values
assert_expression_approximates_to<double>("asin(0)", "0", Degree);
assert_expression_approximates_to<float>("asin(-1)", "-90", Degree);
@@ -527,24 +527,24 @@ QUIZ_CASE(poincare_approximation_trigonometry_functions) {
// Symmetry: odd
assert_expression_approximates_to<double>("atan(-2)", "-1.1071487177941", Radian);
// On [-𝐢, 𝐢]
assert_expression_approximates_to<float>("atan(0.2×𝐢)", "0.202733𝐢", Radian, Cartesian, 6);
assert_expression_approximates_to<float>("atan(0.2×𝐢)", "0.202733×𝐢", Radian, Cartesian, 6);
// Symmetry: odd
assert_expression_approximates_to<float>("atan(-0.2×𝐢)", "-0.202733𝐢", Radian, Cartesian, 6);
assert_expression_approximates_to<float>("atan(-0.2×𝐢)", "-0.202733×𝐢", Radian, Cartesian, 6);
// On [𝐢, inf×𝐢[
assert_expression_approximates_to<double>("atan(26×𝐢)", "1.5707963267949+3.8480520568064ᴇ-2𝐢", Radian);
assert_expression_approximates_to<double>("atan(26×𝐢)", "90+2.2047714220164𝐢", Degree);
assert_expression_approximates_to<double>("atan(26×𝐢)", "1.5707963267949+3.8480520568064ᴇ-2×𝐢", Radian);
assert_expression_approximates_to<double>("atan(26×𝐢)", "90+2.2047714220164×𝐢", Degree);
// Symmetry: odd
assert_expression_approximates_to<double>("atan(-26×𝐢)", "-1.5707963267949-3.8480520568064ᴇ-2𝐢", Radian);
assert_expression_approximates_to<double>("atan(-26×𝐢)", "-1.5707963267949-3.8480520568064ᴇ-2×𝐢", Radian);
// On ]-inf×𝐢, -𝐢[
assert_expression_approximates_to<float>("atan(-3.4×𝐢)", "-1.570796-0.3030679𝐢", Radian);
assert_expression_approximates_to<float>("atan(-3.4×𝐢)", "-90-17.3645𝐢", Degree, Cartesian, 6);
assert_expression_approximates_to<float>("atan(-3.4×𝐢)", "-1.570796-0.3030679×𝐢", Radian);
assert_expression_approximates_to<float>("atan(-3.4×𝐢)", "-90-17.3645×𝐢", Degree, Cartesian, 6);
// On C
assert_expression_approximates_to<float>("atan(𝐢-4)", "-1.338973+0.05578589𝐢", Radian);
assert_expression_approximates_to<float>("atan(𝐢-4)", "-76.7175+3.1963𝐢", Degree, Cartesian, 6);
assert_expression_approximates_to<float>("atan(𝐢-4)", "-1.338973+0.05578589×𝐢", Radian);
assert_expression_approximates_to<float>("atan(𝐢-4)", "-76.7175+3.1963×𝐢", Degree, Cartesian, 6);
// Key values
assert_expression_approximates_to<float>("atan(0)", "0", Degree);
assert_expression_approximates_to<double>("atan(-𝐢)", "-inf𝐢", Radian);
assert_expression_approximates_to<double>("atan(𝐢)", "inf𝐢", Radian);
assert_expression_approximates_to<double>("atan(-𝐢)", "-inf×𝐢", Radian);
assert_expression_approximates_to<double>("atan(𝐢)", "inf×𝐢", Radian);
/* cosh: R -> R (even)
* R×𝐢 -> R (oscillator)
@@ -563,8 +563,8 @@ QUIZ_CASE(poincare_approximation_trigonometry_functions) {
assert_expression_approximates_to<float>("cosh(8×π×𝐢/2)", "1", Radian);
assert_expression_approximates_to<float>("cosh(9×π×𝐢/2)", "0", Radian);
// On C
assert_expression_approximates_to<float>("cosh(𝐢-4)", "14.7547-22.9637𝐢", Radian, Cartesian, 6);
assert_expression_approximates_to<float>("cosh(𝐢-4)", "14.7547-22.9637𝐢", Degree, Cartesian, 6);
assert_expression_approximates_to<float>("cosh(𝐢-4)", "14.7547-22.9637×𝐢", Radian, Cartesian, 6);
assert_expression_approximates_to<float>("cosh(𝐢-4)", "14.7547-22.9637×𝐢", Degree, Cartesian, 6);
/* sinh: R -> R (odd)
* R×𝐢 -> R×𝐢 (oscillator)
@@ -575,7 +575,7 @@ QUIZ_CASE(poincare_approximation_trigonometry_functions) {
// Symmetry: odd
assert_expression_approximates_to<double>("sinh(-2)", "-3.626860407847", Radian);
// On R×𝐢
assert_expression_approximates_to<double>("sinh(43×𝐢)", "-0.8317747426286𝐢", Radian);
assert_expression_approximates_to<double>("sinh(43×𝐢)", "-0.8317747426286×𝐢", Radian);
// Oscillator
assert_expression_approximates_to<float>("sinh(π×𝐢/2)", "𝐢", Radian);
assert_expression_approximates_to<float>("sinh(5×π×𝐢/2)", "𝐢", Radian);
@@ -583,8 +583,8 @@ QUIZ_CASE(poincare_approximation_trigonometry_functions) {
assert_expression_approximates_to<float>("sinh(8×π×𝐢/2)", "0", Radian);
assert_expression_approximates_to<float>("sinh(9×π×𝐢/2)", "𝐢", Radian);
// On C
assert_expression_approximates_to<float>("sinh(𝐢-4)", "-14.7448+22.9791𝐢", Radian, Cartesian, 6);
assert_expression_approximates_to<float>("sinh(𝐢-4)", "-14.7448+22.9791𝐢", Degree, Cartesian, 6);
assert_expression_approximates_to<float>("sinh(𝐢-4)", "-14.7448+22.9791×𝐢", Radian, Cartesian, 6);
assert_expression_approximates_to<float>("sinh(𝐢-4)", "-14.7448+22.9791×𝐢", Degree, Cartesian, 6);
/* tanh: R -> R (odd)
* R×𝐢 -> R×𝐢 (tangent-style)
@@ -594,7 +594,7 @@ QUIZ_CASE(poincare_approximation_trigonometry_functions) {
// Symmetry: odd
assert_expression_approximates_to<double>("tanh(-2)", "-9.6402758007582ᴇ-1", Degree);
// On R×i
assert_expression_approximates_to<double>("tanh(43×𝐢)", "-1.4983873388552𝐢", Radian);
assert_expression_approximates_to<double>("tanh(43×𝐢)", "-1.4983873388552×𝐢", Radian);
// Tangent-style
// FIXME: this depends on the libm implementation and does not work on travis/appveyor servers
/*assert_expression_approximates_to<float>("tanh(π×𝐢/2)", Undefined::Name(), Radian);
@@ -603,8 +603,8 @@ QUIZ_CASE(poincare_approximation_trigonometry_functions) {
assert_expression_approximates_to<float>("tanh(8×π×𝐢/2)", "0", Radian);
assert_expression_approximates_to<float>("tanh(9×π×𝐢/2)", Undefined::Name(), Radian);*/
// On C
assert_expression_approximates_to<float>("tanh(𝐢-4)", "-1.00028+0.000610241𝐢", Radian, Cartesian, 6);
assert_expression_approximates_to<float>("tanh(𝐢-4)", "-1.00028+0.000610241𝐢", Degree, Cartesian, 6);
assert_expression_approximates_to<float>("tanh(𝐢-4)", "-1.00028+0.000610241×𝐢", Radian, Cartesian, 6);
assert_expression_approximates_to<float>("tanh(𝐢-4)", "-1.00028+0.000610241×𝐢", Degree, Cartesian, 6);
/* acosh: [-1,1] -> R×𝐢
* ]-inf,-1[ -> π×𝐢+R (even on real)
@@ -616,24 +616,24 @@ QUIZ_CASE(poincare_approximation_trigonometry_functions) {
assert_expression_approximates_to<double>("acosh(2)", "1.3169578969248", Radian);
assert_expression_approximates_to<double>("acosh(2)", "1.3169578969248", Degree);
// On ]-inf, -1[
assert_expression_approximates_to<double>("acosh(-4)", "2.0634370688956+3.1415926535898𝐢", Radian);
assert_expression_approximates_to<float>("acosh(-4)", "2.06344+3.14159𝐢", Radian, Cartesian, 6);
assert_expression_approximates_to<double>("acosh(-4)", "2.0634370688956+3.1415926535898×𝐢", Radian);
assert_expression_approximates_to<float>("acosh(-4)", "2.06344+3.14159×𝐢", Radian, Cartesian, 6);
// On ]1,inf[: Symmetry: even on real
assert_expression_approximates_to<double>("acosh(4)", "2.0634370688956", Radian);
assert_expression_approximates_to<float>("acosh(4)", "2.063437", Radian);
// On ]-inf×𝐢, 0[
assert_expression_approximates_to<double>("acosh(-42×𝐢)", "4.4309584920805-1.5707963267949𝐢", Radian);
assert_expression_approximates_to<float>("acosh(-42×𝐢)", "4.431-1.571𝐢", Radian, Cartesian, 4);
assert_expression_approximates_to<double>("acosh(-42×𝐢)", "4.4309584920805-1.5707963267949×𝐢", Radian);
assert_expression_approximates_to<float>("acosh(-42×𝐢)", "4.431-1.571×𝐢", Radian, Cartesian, 4);
// On ]0, 𝐢×inf[: Symmetry: even on real
assert_expression_approximates_to<double>("acosh(42×𝐢)", "4.4309584920805+1.5707963267949𝐢", Radian);
assert_expression_approximates_to<float>("acosh(42×𝐢)", "4.431+1.571𝐢", Radian, Cartesian, 4);
assert_expression_approximates_to<double>("acosh(42×𝐢)", "4.4309584920805+1.5707963267949×𝐢", Radian);
assert_expression_approximates_to<float>("acosh(42×𝐢)", "4.431+1.571×𝐢", Radian, Cartesian, 4);
// On C
assert_expression_approximates_to<float>("acosh(𝐢-4)", "2.0966+2.8894𝐢", Radian, Cartesian, 5);
assert_expression_approximates_to<float>("acosh(𝐢-4)", "2.0966+2.8894𝐢", Degree, Cartesian, 5);
assert_expression_approximates_to<float>("acosh(𝐢-4)", "2.0966+2.8894×𝐢", Radian, Cartesian, 5);
assert_expression_approximates_to<float>("acosh(𝐢-4)", "2.0966+2.8894×𝐢", Degree, Cartesian, 5);
// Key values
//assert_expression_approximates_to<double>("acosh(-1)", "3.1415926535898𝐢", Radian);
//assert_expression_approximates_to<double>("acosh(-1)", "3.1415926535898×𝐢", Radian);
assert_expression_approximates_to<double>("acosh(1)", "0", Radian);
assert_expression_approximates_to<float>("acosh(0)", "1.570796𝐢", Radian);
assert_expression_approximates_to<float>("acosh(0)", "1.570796×𝐢", Radian);
/* asinh: R -> R (odd)
* [-𝐢,𝐢] -> R*𝐢 (odd)
@@ -647,20 +647,20 @@ QUIZ_CASE(poincare_approximation_trigonometry_functions) {
assert_expression_approximates_to<double>("asinh(-2)", "-1.4436354751788", Radian);
assert_expression_approximates_to<double>("asinh(-2)", "-1.4436354751788", Degree);
// On [-𝐢,𝐢]
assert_expression_approximates_to<double>("asinh(0.2×𝐢)", "2.0135792079033ᴇ-1𝐢", Radian);
assert_expression_approximates_to<float>("asinh(0.2×𝐢)", "0.2013579𝐢", Degree);
assert_expression_approximates_to<double>("asinh(0.2×𝐢)", "2.0135792079033ᴇ-1×𝐢", Radian);
assert_expression_approximates_to<float>("asinh(0.2×𝐢)", "0.2013579×𝐢", Degree);
// Symmetry: odd
assert_expression_approximates_to<double>("asinh(-0.2×𝐢)", "-2.0135792079033ᴇ-1𝐢", Radian);
assert_expression_approximates_to<float>("asinh(-0.2×𝐢)", "-0.2013579𝐢", Degree);
assert_expression_approximates_to<double>("asinh(-0.2×𝐢)", "-2.0135792079033ᴇ-1×𝐢", Radian);
assert_expression_approximates_to<float>("asinh(-0.2×𝐢)", "-0.2013579×𝐢", Degree);
// On ]-inf×𝐢, -𝐢[
assert_expression_approximates_to<double>("asinh(-22×𝐢)", "-3.7836727043295-1.5707963267949𝐢", Radian);
assert_expression_approximates_to<float>("asinh(-22×𝐢)", "-3.784-1.571𝐢", Degree, Cartesian, 4);
assert_expression_approximates_to<double>("asinh(-22×𝐢)", "-3.7836727043295-1.5707963267949×𝐢", Radian);
assert_expression_approximates_to<float>("asinh(-22×𝐢)", "-3.784-1.571×𝐢", Degree, Cartesian, 4);
// On ]𝐢, inf×𝐢[, Symmetry: odd
assert_expression_approximates_to<double>("asinh(22×𝐢)", "3.7836727043295+1.5707963267949𝐢", Radian);
assert_expression_approximates_to<float>("asinh(22×𝐢)", "3.784+1.571𝐢", Degree, Cartesian, 4);
assert_expression_approximates_to<double>("asinh(22×𝐢)", "3.7836727043295+1.5707963267949×𝐢", Radian);
assert_expression_approximates_to<float>("asinh(22×𝐢)", "3.784+1.571×𝐢", Degree, Cartesian, 4);
// On C
assert_expression_approximates_to<float>("asinh(𝐢-4)", "-2.123+0.2383𝐢", Radian, Cartesian, 4);
assert_expression_approximates_to<float>("asinh(𝐢-4)", "-2.123+0.2383𝐢", Degree, Cartesian, 4);
assert_expression_approximates_to<float>("asinh(𝐢-4)", "-2.123+0.2383×𝐢", Radian, Cartesian, 4);
assert_expression_approximates_to<float>("asinh(𝐢-4)", "-2.123+0.2383×𝐢", Degree, Cartesian, 4);
/* atanh: [-1,1] -> R (odd)
* ]-inf,-1[ -> π/2*𝐢+R (odd)
@@ -674,31 +674,31 @@ QUIZ_CASE(poincare_approximation_trigonometry_functions) {
assert_expression_approximates_to<double>("atanh(-0.4)", "-0.4236489301936", Radian);
assert_expression_approximates_to<double>("atanh(-0.4)", "-0.4236489301936", Degree);
// On ]1, inf[
assert_expression_approximates_to<double>("atanh(4)", "0.255412811883-1.5707963267949𝐢", Radian);
assert_expression_approximates_to<float>("atanh(4)", "0.2554128-1.570796𝐢", Degree);
assert_expression_approximates_to<double>("atanh(4)", "0.255412811883-1.5707963267949×𝐢", Radian);
assert_expression_approximates_to<float>("atanh(4)", "0.2554128-1.570796×𝐢", Degree);
// On ]-inf,-1[, Symmetry: odd
assert_expression_approximates_to<double>("atanh(-4)", "-0.255412811883+1.5707963267949𝐢", Radian);
assert_expression_approximates_to<float>("atanh(-4)", "-0.2554128+1.570796𝐢", Degree);
assert_expression_approximates_to<double>("atanh(-4)", "-0.255412811883+1.5707963267949×𝐢", Radian);
assert_expression_approximates_to<float>("atanh(-4)", "-0.2554128+1.570796×𝐢", Degree);
// On R×𝐢
assert_expression_approximates_to<double>("atanh(4×𝐢)", "1.325817663668𝐢", Radian);
assert_expression_approximates_to<float>("atanh(4×𝐢)", "1.325818𝐢", Radian);
assert_expression_approximates_to<double>("atanh(4×𝐢)", "1.325817663668×𝐢", Radian);
assert_expression_approximates_to<float>("atanh(4×𝐢)", "1.325818×𝐢", Radian);
// Symmetry: odd
assert_expression_approximates_to<double>("atanh(-4×𝐢)", "-1.325817663668𝐢", Radian);
assert_expression_approximates_to<float>("atanh(-4×𝐢)", "-1.325818𝐢", Radian);
assert_expression_approximates_to<double>("atanh(-4×𝐢)", "-1.325817663668×𝐢", Radian);
assert_expression_approximates_to<float>("atanh(-4×𝐢)", "-1.325818×𝐢", Radian);
// On C
assert_expression_approximates_to<float>("atanh(𝐢-4)", "-0.238878+1.50862𝐢", Radian, Cartesian, 6);
assert_expression_approximates_to<float>("atanh(𝐢-4)", "-0.238878+1.50862𝐢", Degree, Cartesian, 6);
assert_expression_approximates_to<float>("atanh(𝐢-4)", "-0.238878+1.50862×𝐢", Radian, Cartesian, 6);
assert_expression_approximates_to<float>("atanh(𝐢-4)", "-0.238878+1.50862×𝐢", Degree, Cartesian, 6);
// WARNING: evaluate on branch cut can be multivalued
assert_expression_approximates_to<double>("acos(2)", "1.3169578969248𝐢", Radian);
assert_expression_approximates_to<double>("acos(2)", "75.456129290217𝐢", Degree);
assert_expression_approximates_to<double>("asin(2)", "1.5707963267949-1.3169578969248𝐢", Radian);
assert_expression_approximates_to<double>("asin(2)", "90-75.456129290217𝐢", Degree);
assert_expression_approximates_to<double>("atanh(2)", "5.4930614433405ᴇ-1-1.5707963267949𝐢", Radian);
assert_expression_approximates_to<double>("atan(2𝐢)", "1.5707963267949+5.4930614433405ᴇ-1𝐢", Radian);
assert_expression_approximates_to<double>("atan(2𝐢)", "90+31.472923730945𝐢", Degree);
assert_expression_approximates_to<double>("asinh(2𝐢)", "1.3169578969248+1.5707963267949𝐢", Radian);
assert_expression_approximates_to<double>("acosh(-2)", "1.3169578969248+3.1415926535898𝐢", Radian);
assert_expression_approximates_to<double>("acos(2)", "1.3169578969248×𝐢", Radian);
assert_expression_approximates_to<double>("acos(2)", "75.456129290217×𝐢", Degree);
assert_expression_approximates_to<double>("asin(2)", "1.5707963267949-1.3169578969248×𝐢", Radian);
assert_expression_approximates_to<double>("asin(2)", "90-75.456129290217×𝐢", Degree);
assert_expression_approximates_to<double>("atanh(2)", "5.4930614433405ᴇ-1-1.5707963267949×𝐢", Radian);
assert_expression_approximates_to<double>("atan(2𝐢)", "1.5707963267949+5.4930614433405ᴇ-1×𝐢", Radian);
assert_expression_approximates_to<double>("atan(2𝐢)", "90+31.472923730945×𝐢", Degree);
assert_expression_approximates_to<double>("asinh(2𝐢)", "1.3169578969248+1.5707963267949×𝐢", Radian);
assert_expression_approximates_to<double>("acosh(-2)", "1.3169578969248+3.1415926535898×𝐢", Radian);
}
QUIZ_CASE(poincare_approximation_matrix) {
@@ -764,7 +764,7 @@ QUIZ_CASE(poincare_approximation_complex_format) {
assert_expression_approximates_to<double>("0.1", "0.1", Radian, Cartesian);
assert_expression_approximates_to<float>("0.1234567", "0.1234567", Radian, Cartesian);
assert_expression_approximates_to<double>("0.123456789012345", "1.2345678901235ᴇ-1", Radian, Cartesian);
assert_expression_approximates_to<float>("1+2×𝐢", "1+2𝐢", Radian, Cartesian);
assert_expression_approximates_to<float>("1+2×𝐢", "1+2×𝐢", Radian, Cartesian);
assert_expression_approximates_to<double>("1+𝐢-𝐢", "1", Radian, Cartesian);
assert_expression_approximates_to<float>("1+𝐢-1", "𝐢", Radian, Cartesian);
assert_expression_approximates_to<double>("1+𝐢", "1+𝐢", Radian, Cartesian);
@@ -774,53 +774,53 @@ QUIZ_CASE(poincare_approximation_complex_format) {
assert_expression_approximates_to<float>("𝐢", "𝐢", Radian, Cartesian);
assert_expression_approximates_to<double>("√(-1)", "𝐢", Radian, Cartesian);
assert_expression_approximates_to<double>("√(-1)×√(-1)", "-1", Radian, Cartesian);
assert_expression_approximates_to<double>("ln(-2)", "6.9314718055995ᴇ-1+3.1415926535898𝐢", Radian, Cartesian);
assert_expression_approximates_to<double>("(-8)^(1/3)", "1+1.7320508075689𝐢", Radian, Cartesian);
assert_expression_approximates_to<float>("(-8)^(2/3)", "-2+3.4641𝐢", Radian, Cartesian, 6);
assert_expression_approximates_to<double>("root(-8,3)", "1+1.7320508075689𝐢", Radian, Cartesian);
assert_expression_approximates_to<double>("ln(-2)", "6.9314718055995ᴇ-1+3.1415926535898×𝐢", Radian, Cartesian);
assert_expression_approximates_to<double>("(-8)^(1/3)", "1+1.7320508075689×𝐢", Radian, Cartesian);
assert_expression_approximates_to<float>("(-8)^(2/3)", "-2+3.4641×𝐢", Radian, Cartesian, 6);
assert_expression_approximates_to<double>("root(-8,3)", "1+1.7320508075689×𝐢", Radian, Cartesian);
// Polar
assert_expression_approximates_to<float>("0", "0", Radian, Polar);
assert_expression_approximates_to<double>("0", "0", Radian, Polar);
assert_expression_approximates_to<float>("10", "10", Radian, Polar);
assert_expression_approximates_to<double>("-10", "10ℯ^\u00123.1415926535898𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<double>("-10", "10×ℯ^\u00123.1415926535898×𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<float>("100", "100", Radian, Polar);
assert_expression_approximates_to<double>("0.1", "0.1", Radian, Polar);
assert_expression_approximates_to<float>("0.1234567", "0.1234567", Radian, Polar);
assert_expression_approximates_to<double>("0.12345678", "0.12345678", Radian, Polar);
assert_expression_approximates_to<float>("1+2×𝐢", "2.236068ℯ^\u00121.107149𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<float>("1+2×𝐢", "2.236068×ℯ^\u00121.107149×𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<float>("1+𝐢-𝐢", "1", Radian, Polar);
assert_expression_approximates_to<double>("1+𝐢-1", "ℯ^\u00121.57079632679𝐢\u0013", Radian, Polar, 12);
assert_expression_approximates_to<float>("1+𝐢", "1.414214ℯ^\u00120.7853982𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<double>("3+𝐢", "3.16227766017ℯ^\u00120.321750554397𝐢\u0013", Radian, Polar,12);
assert_expression_approximates_to<float>("3-𝐢", "3.162278ℯ^\u0012-0.3217506𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<double>("3-𝐢-3", "ℯ^\u0012-1.57079632679𝐢\u0013", Radian, Polar,12);
assert_expression_approximates_to<float>("2ℯ^(𝐢)", "2ℯ^𝐢", Radian, Polar, 5);
assert_expression_approximates_to<double>("2ℯ^(-𝐢)", "2ℯ^\u0012-𝐢\u0013", Radian, Polar, 5);
assert_expression_approximates_to<double>("1+𝐢-1", "ℯ^\u00121.57079632679×𝐢\u0013", Radian, Polar, 12);
assert_expression_approximates_to<float>("1+𝐢", "1.414214×ℯ^\u00120.7853982×𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<double>("3+𝐢", "3.16227766017×ℯ^\u00120.321750554397×𝐢\u0013", Radian, Polar,12);
assert_expression_approximates_to<float>("3-𝐢", "3.162278×ℯ^\u0012-0.3217506×𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<double>("3-𝐢-3", "ℯ^\u0012-1.57079632679×𝐢\u0013", Radian, Polar,12);
assert_expression_approximates_to<float>("2ℯ^(𝐢)", "2×ℯ^𝐢", Radian, Polar, 5);
assert_expression_approximates_to<double>("2ℯ^(-𝐢)", "2×ℯ^\u0012-𝐢\u0013", Radian, Polar, 5);
assert_expression_approximates_to<float>("𝐢", "ℯ^\u00121.570796𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<double>("√(-1)", "ℯ^\u00121.5707963267949𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<double>("√(-1)×√(-1)", "ℯ^\u00123.1415926535898𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<double>("(-8)^(1/3)", "2ℯ^\u00121.0471975511966𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<float>("(-8)^(2/3)", "4ℯ^\u00122.094395𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<double>("root(-8,3)", "2ℯ^\u00121.0471975511966𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<float>("𝐢", "ℯ^\u00121.570796×𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<double>("√(-1)", "ℯ^\u00121.5707963267949×𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<double>("√(-1)×√(-1)", "ℯ^\u00123.1415926535898×𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<double>("(-8)^(1/3)", "2×ℯ^\u00121.0471975511966×𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<float>("(-8)^(2/3)", "4×ℯ^\u00122.094395×𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<double>("root(-8,3)", "2×ℯ^\u00121.0471975511966×𝐢\u0013", Radian, Polar);
// Cartesian to Polar and vice versa
assert_expression_approximates_to<double>("2+3×𝐢", "3.60555127546ℯ^\u00120.982793723247𝐢\u0013", Radian, Polar, 12);
assert_expression_approximates_to<double>("3.60555127546ℯ^(0.982793723247×𝐢)", "2+3𝐢", Radian, Cartesian, 12);
assert_expression_approximates_to<float>("12.04159457879229548012824103ℯ^(1.4876550949×𝐢)", "1+12𝐢", Radian, Cartesian, 5);
assert_expression_approximates_to<double>("2+3×𝐢", "3.60555127546×ℯ^\u00120.982793723247×𝐢\u0013", Radian, Polar, 12);
assert_expression_approximates_to<double>("3.60555127546×ℯ^(0.982793723247×𝐢)", "2+3×𝐢", Radian, Cartesian, 12);
assert_expression_approximates_to<float>("12.04159457879229548012824103×ℯ^(1.4876550949×𝐢)", "1+12×𝐢", Radian, Cartesian, 5);
// Overflow
assert_expression_approximates_to<float>("-2ᴇ20+2ᴇ20×𝐢", "-2ᴇ20+2ᴇ20𝐢", Radian, Cartesian);
assert_expression_approximates_to<float>("-2ᴇ20+2ᴇ20×𝐢", "2.828427ᴇ20ℯ^\u00122.356194𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<double>("1ᴇ155-1ᴇ155×𝐢", "1ᴇ155-1ᴇ155𝐢", Radian, Cartesian);
assert_expression_approximates_to<double>("1ᴇ155-1ᴇ155×𝐢", "1.41421356237ᴇ155ℯ^\u0012-0.785398163397𝐢\u0013", Radian, Polar,12);
assert_expression_approximates_to<float>("-2ᴇ20+2ᴇ20×𝐢", "-2ᴇ20+2ᴇ20×𝐢", Radian, Cartesian);
assert_expression_approximates_to<float>("-2ᴇ20+2ᴇ20×𝐢", "2.828427ᴇ20×ℯ^\u00122.356194×𝐢\u0013", Radian, Polar);
assert_expression_approximates_to<double>("1ᴇ155-1ᴇ155×𝐢", "1ᴇ155-1ᴇ155×𝐢", Radian, Cartesian);
assert_expression_approximates_to<double>("1ᴇ155-1ᴇ155×𝐢", "1.41421356237ᴇ155×ℯ^\u0012-0.785398163397×𝐢\u0013", Radian, Polar,12);
assert_expression_approximates_to<float>("-2ᴇ100+2ᴇ100×𝐢", Undefined::Name());
assert_expression_approximates_to<double>("-2ᴇ360+2ᴇ360×𝐢", Undefined::Name());
assert_expression_approximates_to<float>("-2ᴇ100+2ᴇ10×𝐢", "-inf+2ᴇ10𝐢");
assert_expression_approximates_to<double>("-2ᴇ360+2×𝐢", "-inf+2𝐢");
assert_expression_approximates_to<float>("-2ᴇ100+2ᴇ10×𝐢", "-inf+2ᴇ10×𝐢");
assert_expression_approximates_to<double>("-2ᴇ360+2×𝐢", "-inf+2×𝐢");
assert_expression_approximates_to<float>("undef+2ᴇ100×𝐢", Undefined::Name());
assert_expression_approximates_to<double>("-2ᴇ360+undef×𝐢", Undefined::Name());
}

216
poincare/test/simplification.cpp
View File

@@ -86,10 +86,10 @@ QUIZ_CASE(poincare_simplification_infinity) {
assert_parsed_expression_simplify_to("inf^2", "inf");
assert_parsed_expression_simplify_to("(-inf)^2", "inf");
assert_parsed_expression_simplify_to("inf^√(2)", "inf");
assert_parsed_expression_simplify_to("(-inf)^√(2)", "inf(-1)^√(2)");
assert_parsed_expression_simplify_to("(-inf)^√(2)", "inf×(-1)^√(2)");
assert_parsed_expression_simplify_to("inf^x", "inf^x");
assert_parsed_expression_simplify_to("1/inf+24", "24");
assert_parsed_expression_simplify_to("ℯ^(inf)/inf", "0ℯ^inf");
assert_parsed_expression_simplify_to("ℯ^(inf)/inf", "0×ℯ^inf");
// Logarithm
assert_parsed_expression_simplify_to("log(inf,0)", "undef");
@@ -121,7 +121,7 @@ QUIZ_CASE(poincare_simplification_addition) {
assert_parsed_expression_simplify_to("-2-6", "-8");
assert_parsed_expression_simplify_to("-A", "-A");
assert_parsed_expression_simplify_to("A-A", "0");
assert_parsed_expression_simplify_to("-5π+3π", "-2π");
assert_parsed_expression_simplify_to("-5π+3π", "-2×π");
assert_parsed_expression_simplify_to("1-3+A-5+2A-4A", "-A-7");
assert_parsed_expression_simplify_to("A+B-A-B", "0");
assert_parsed_expression_simplify_to("A+B+(-1)×A+(-1)×B", "0");
@@ -134,8 +134,8 @@ QUIZ_CASE(poincare_simplification_addition) {
assert_parsed_expression_simplify_to("1/x^2+1/(x^2×π)", "\u0012π+1\u0013/\u0012π×x^2\u0013");
assert_parsed_expression_simplify_to("1/x^2+1/(x^3×π)", "\u0012π×x+1\u0013/\u0012π×x^3\u0013");
assert_parsed_expression_simplify_to("4x/x^2+3π/(x^3×π)", "\u00124×x^2+3\u0013/x^3");
assert_parsed_expression_simplify_to("3^(1/2)+2^(-2×3^(1/2)×ℯ^π)/2", "\u00122×\u00122^\u00122√(3)ℯ^π\u0013\u0013√(3)+1\u0013/\u00122×2^\u00122√(3)ℯ^π\u0013\u0013");
assert_parsed_expression_simplify_to("[[1,2+𝐢][3,4][5,6]]+[[1,2+𝐢][3,4][5,6]]", "[[2,4+2𝐢][6,8][10,12]]");
assert_parsed_expression_simplify_to("3^(1/2)+2^(-2×3^(1/2)×ℯ^π)/2", "\u00122×2^\u00122×√(3)×ℯ^π\u0013×√(3)+1\u0013/\u00122×2^\u00122×√(3)×ℯ^π\u0013\u0013");
assert_parsed_expression_simplify_to("[[1,2+𝐢][3,4][5,6]]+[[1,2+𝐢][3,4][5,6]]", "[[2,4+2×𝐢][6,8][10,12]]");
assert_parsed_expression_simplify_to("3+[[1,2][3,4]]", "undef");
assert_parsed_expression_simplify_to("[[1][3][5]]+[[1,2+𝐢][3,4][5,6]]", "undef");
assert_parsed_expression_simplify_to("[[1,3]]+confidence(π/4, 6)+[[2,3]]", "[[3,6]]+confidence(π/4,6)");
@@ -178,8 +178,8 @@ QUIZ_CASE(poincare_simplification_multiplication) {
assert_parsed_expression_simplify_to("(x+1)×(x+2)", "x^2+3×x+2");
assert_parsed_expression_simplify_to("(x+1)×(x-1)", "x^2-1");
assert_parsed_expression_simplify_to("11π/(22π+11π)", "1/3");
assert_parsed_expression_simplify_to("11/(22π+11π)", "1/3π");
assert_parsed_expression_simplify_to("-11/(22π+11π)", "-1/3π");
assert_parsed_expression_simplify_to("11/(22π+11π)", "1/\u00123×π\u0013");
assert_parsed_expression_simplify_to("-11/(22π+11π)", "-1/\u00123×π\u0013");
assert_parsed_expression_simplify_to("A^2×B×A^(-2)×B^(-2)", "1/B");
assert_parsed_expression_simplify_to("A^(-1)×B^(-1)", "1/\u0012A×B\u0013");
assert_parsed_expression_simplify_to("x+x", "2×x");
@@ -191,11 +191,11 @@ QUIZ_CASE(poincare_simplification_multiplication) {
assert_parsed_expression_simplify_to("x-x-n+n", "0");
assert_parsed_expression_simplify_to("x+n-x-n", "0");
assert_parsed_expression_simplify_to("x-x", "0");
assert_parsed_expression_simplify_to("π×3^(1/2)×(5π)^(1/2)×(4/5)^(1/2)", "2√(3)π^\u00123/2\u0013");
assert_parsed_expression_simplify_to("12^(1/4)×(π/6)×(12×π)^(1/4)", "√(3)π^\u00125/4\u0013/3");
assert_parsed_expression_simplify_to("[[1,2+𝐢][3,4][5,6]]×[[1,2+𝐢,3,4][5,6+𝐢,7,8]]", "[[11+5𝐢,13+9𝐢,17+7𝐢,20+8𝐢][23,30+7𝐢,37,44][35,46+11𝐢,57,68]]");
assert_parsed_expression_simplify_to("π×3^(1/2)×(5π)^(1/2)×(4/5)^(1/2)", "2×√(3)×π^\u00123/2\u0013");
assert_parsed_expression_simplify_to("12^(1/4)×(π/6)×(12×π)^(1/4)", "\u0012√(3)×π^\u00125/4\u0013\u0013/3");
assert_parsed_expression_simplify_to("[[1,2+𝐢][3,4][5,6]]×[[1,2+𝐢,3,4][5,6+𝐢,7,8]]", "[[11+5×𝐢,13+9×𝐢,17+7×𝐢,20+8×𝐢][23,30+7×𝐢,37,44][35,46+11×𝐢,57,68]]");
assert_parsed_expression_simplify_to("[[1,2][3,4]]×[[1,3][5,6]]×[[2,3][4,6]]", "[[82,123][178,267]]");
assert_parsed_expression_simplify_to("π×confidence(π/5,3)[[1,2]]", "π×confidence(π/5,3)[[1,2]]");
assert_parsed_expression_simplify_to("π×confidence(π/5,3)[[1,2]]", "π×confidence(π/5,3)×[[1,2]]");
}
QUIZ_CASE(poincare_simplification_power) {
@@ -212,14 +212,14 @@ QUIZ_CASE(poincare_simplification_power) {
assert_parsed_expression_simplify_to("0^0", Undefined::Name());
assert_parsed_expression_simplify_to("0^(-3)", Undefined::Name());
assert_parsed_expression_simplify_to("4^0.5", "2");
assert_parsed_expression_simplify_to("8^0.5", "2√(2)");
assert_parsed_expression_simplify_to("(12^4×3)^(0.5)", "144√(3)");
assert_parsed_expression_simplify_to("8^0.5", "2×√(2)");
assert_parsed_expression_simplify_to("(12^4×3)^(0.5)", "144×√(3)");
assert_parsed_expression_simplify_to("(π^3)^4", "π^12");
assert_parsed_expression_simplify_to("(A×B)^3", "A^3×B^3");
assert_parsed_expression_simplify_to("(12^4×x)^(0.5)", "144√(x)");
assert_parsed_expression_simplify_to("√(32)", "4√(2)");
assert_parsed_expression_simplify_to("(12^4×x)^(0.5)", "144×√(x)");
assert_parsed_expression_simplify_to("√(32)", "4×√(2)");
assert_parsed_expression_simplify_to("√(-1)", "𝐢");
assert_parsed_expression_simplify_to("√(-1×√(-1))", "√(2)/2-\u0012√(2)/2\u0013𝐢");
assert_parsed_expression_simplify_to("√(-1×√(-1))", "√(2)/2-√(2)/2×𝐢");
assert_parsed_expression_simplify_to("√(3^2)", "3");
assert_parsed_expression_simplify_to("2^(2+π)", "4×2^π");
assert_parsed_expression_simplify_to("√(5513219850886344455940081)", "2348024669991");
@@ -227,10 +227,10 @@ QUIZ_CASE(poincare_simplification_power) {
assert_parsed_expression_simplify_to("√(π)^2", "π");
assert_parsed_expression_simplify_to("√(π^2)", "π");
assert_parsed_expression_simplify_to("√((-π)^2)", "π");
assert_parsed_expression_simplify_to("√(x×144)", "12√(x)");
assert_parsed_expression_simplify_to("√(x×144×π^2)", "12π√(x)");
assert_parsed_expression_simplify_to("√(x×144×π)", "12√(π)√(x)");
assert_parsed_expression_simplify_to("(-1)×(2+(-4×√(2)))", "4√(2)-2");
assert_parsed_expression_simplify_to("√(x×144)", "12×√(x)");
assert_parsed_expression_simplify_to("√(x×144×π^2)", "12×π×√(x)");
assert_parsed_expression_simplify_to("√(x×144×π)", "12×√(π)×√(x)");
assert_parsed_expression_simplify_to("(-1)×(2+(-4×√(2)))", "4×√(2)-2");
assert_parsed_expression_simplify_to("x^(1/2)", "√(x)");
assert_parsed_expression_simplify_to("x^(-1/2)", "1/√(x)");
assert_parsed_expression_simplify_to("x^(1/7)", "root(x,7)");
@@ -241,7 +241,7 @@ QUIZ_CASE(poincare_simplification_power) {
assert_parsed_expression_simplify_to("π^log(√(3),π)", "√(3)");
assert_parsed_expression_simplify_to("10^log(π)", "π");
assert_parsed_expression_simplify_to("ℯ^ln(65)", "65");
assert_parsed_expression_simplify_to("ℯ^ln(πℯ)", "πℯ");
assert_parsed_expression_simplify_to("ℯ^ln(πℯ)", "π×ℯ");
assert_parsed_expression_simplify_to("ℯ^log(πℯ)", "ℯ^\u0012log(ℯ)+log(π)\u0013");
assert_parsed_expression_simplify_to("√(ℯ^2)", "ℯ");
assert_parsed_expression_simplify_to("999^(10000/3)", "999^\u001210000/3\u0013");
@@ -253,21 +253,21 @@ QUIZ_CASE(poincare_simplification_power) {
* factors above k_maxNumberOfPrimeFactors. */
assert_parsed_expression_simplify_to("1002101470343^(1/3)", "root(1002101470343,3)");
assert_parsed_expression_simplify_to("π×π×π", "π^3");
assert_parsed_expression_simplify_to("(x+π)^(3)", "x^3+3π×x^2+3π^2×x+π^3");
assert_parsed_expression_simplify_to("(5+√(2))^(-8)", "\u0012-1003320√(2)+1446241\u0013/78310985281");
assert_parsed_expression_simplify_to("(5×π+√(2))^(-5)", "1/\u00123125π^5+3125√(2)π^4+2500π^3+500√(2)π^2+100π+4√(2)\u0013");
assert_parsed_expression_simplify_to("(1+√(2)+√(3))^5", "120√(6)+184√(3)+224√(2)+296");
assert_parsed_expression_simplify_to("(π+√(2)+√(3)+x)^(-3)", "1/\u0012x^3+3π×x^2+3√(3)×x^2+3√(2)×x^2+3π^2×x+6√(3)π×x+6√(2)π×x+6√(6)×x+15×x+π^3+3√(3)π^2+3√(2)π^2+6√(6)π+15π+9√(3)+11√(2)\u0013");
assert_parsed_expression_simplify_to("(x+π)^(3)", "x^3+3×π×x^2+3×π^2×x+π^3");
assert_parsed_expression_simplify_to("(5+√(2))^(-8)", "\u0012-1003320×√(2)+1446241\u0013/78310985281");
assert_parsed_expression_simplify_to("(5×π+√(2))^(-5)", "1/\u00123125×π^5+3125×√(2)×π^4+2500×π^3+500×√(2)×π^2+100×π+4×√(2)\u0013");
assert_parsed_expression_simplify_to("(1+√(2)+√(3))^5", "120×√(6)+184×√(3)+224×√(2)+296");
assert_parsed_expression_simplify_to("(π+√(2)+√(3)+x)^(-3)", "1/\u0012x^3+3×π×x^2+3×√(3)×x^2+3×√(2)×x^2+3×π^2×x+6×√(3)×π×x+6×√(2)×π×x+6×√(6)×x+15×x+π^3+3×√(3)×π^2+3×√(2)×π^2+6×√(6)×π+15×π+9×√(3)+11×√(2)\u0013");
assert_parsed_expression_simplify_to("1.0066666666667^60", "(10066666666667/10000000000000)^60");
assert_parsed_expression_simplify_to("2^(6+π+x)", "64×2^\u0012x+π\u0013");
assert_parsed_expression_simplify_to("𝐢^(2/3)", "1/2+\u0012√(3)/2\u0013𝐢");
assert_parsed_expression_simplify_to("ℯ^(𝐢×π/3)", "1/2+\u0012√(3)/2\u0013𝐢");
assert_parsed_expression_simplify_to("(-1)^(1/3)", "1/2+\u0012√(3)/2\u0013𝐢");
assert_parsed_expression_simplify_to("𝐢^(2/3)", "1/2+√(3)/2×𝐢");
assert_parsed_expression_simplify_to("ℯ^(𝐢×π/3)", "1/2+√(3)/2×𝐢");
assert_parsed_expression_simplify_to("(-1)^(1/3)", "1/2+√(3)/2×𝐢");
assert_parsed_expression_simplify_to("R(-x)", "R(-x)");
assert_parsed_expression_simplify_to("√(x)^2", "x", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("√(-3)^2", "unreal", User, Radian, Real);
// Principal angle of root of unity
assert_parsed_expression_simplify_to("(-5)^(-1/3)", "1/\u00122×root(5,3)\u0013-\u0012√(3)/\u00122×root(5,3)\u0013\u0013𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("(-5)^(-1/3)", "1/\u00122×root(5,3)\u0013-√(3)/\u00122×root(5,3)\u0013×𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("1+((8+√(6))^(1/2))^-1+(8+√(6))^(1/2)", "\u0012√(√(6)+8)+√(6)+9\u0013/√(√(6)+8)", User, Radian, Real);
assert_parsed_expression_simplify_to("[[1,2][3,4]]^(-3)", "[[-59/4,27/4][81/8,-37/8]]");
assert_parsed_expression_simplify_to("[[1,2][3,4]]^3", "[[37,54][81,118]]");
@@ -302,7 +302,7 @@ QUIZ_CASE(poincare_simplification_logarithm) {
assert_parsed_expression_simplify_to("log(√(3),√(3))", "1");
assert_parsed_expression_simplify_to("log(1/√(2))", "-log(2)/2");
assert_parsed_expression_simplify_to("log(-𝐢)", "log(-𝐢)");
assert_parsed_expression_simplify_to("ln(ℯ^(𝐢π/7))", "\u0012π/7\u0013𝐢");
assert_parsed_expression_simplify_to("ln(ℯ^(𝐢π/7))", "π/7×𝐢");
assert_parsed_expression_simplify_to("log(10^24)", "24");
assert_parsed_expression_simplify_to("log((23π)^4,23π)", "4");
assert_parsed_expression_simplify_to("log(10^(2+π))", "π+2");
@@ -401,22 +401,22 @@ QUIZ_CASE(poincare_simplication_trigonometry_functions) {
assert_parsed_expression_simplify_to("sin(x)/(π×cos(x))", "tan(x)/π");
assert_parsed_expression_simplify_to("1×tan(2)×tan(5)", "tan(2)×tan(5)");
assert_parsed_expression_simplify_to("tan(62π/21)", "-tan(π/21)");
assert_parsed_expression_simplify_to("cos(26π/21)/sin(25π/17)", "cos(5π/21)/sin(8π/17)");
assert_parsed_expression_simplify_to("cos(62π/21)×π×3/sin(62π/21)", "-3π/tan(π/21)");
assert_parsed_expression_simplify_to("cos(62π/21)/(π×3×sin(62π/21))", "-1/\u00123π×tan(π/21)\u0013");
assert_parsed_expression_simplify_to("sin(62π/21)×π×3/cos(62π/21)", "-3π×tan(π/21)");
assert_parsed_expression_simplify_to("sin(62π/21)/(π×3cos(62π/21))", "-tan(π/21)/3π");
assert_parsed_expression_simplify_to("cos(26π/21)/sin(25π/17)", "cos(\u00125×π\u0013/21)/sin(\u00128×π\u0013/17)");
assert_parsed_expression_simplify_to("cos(62π/21)×π×3/sin(62π/21)", "-\u00123×π\u0013/tan(π/21)");
assert_parsed_expression_simplify_to("cos(62π/21)/(π×3×sin(62π/21))", "-1/\u00123×π×tan(π/21)\u0013");
assert_parsed_expression_simplify_to("sin(62π/21)×π×3/cos(62π/21)", "-3×π×tan(π/21)");
assert_parsed_expression_simplify_to("sin(62π/21)/(π×3cos(62π/21))", "-tan(π/21)/\u00123×π\u0013");
assert_parsed_expression_simplify_to("-cos(π/62)ln(3)/(sin(π/62)π)", "-ln(3)/\u0012π×tan(π/62)\u0013");
assert_parsed_expression_simplify_to("-2cos(π/62)ln(3)/(sin(π/62)π)", "-\u00122×ln(3)\u0013/\u0012π×tan(π/62)\u0013");
// -- cos
assert_parsed_expression_simplify_to("cos(0)", "1");
assert_parsed_expression_simplify_to("cos(π)", "-1");
assert_parsed_expression_simplify_to("cos(π×4/7)", "-cos(3π/7)");
assert_parsed_expression_simplify_to("cos(π×35/29)", "-cos(6π/29)");
assert_parsed_expression_simplify_to("cos(-π×35/29)", "-cos(6π/29)");
assert_parsed_expression_simplify_to("cos(π×4/7)", "-cos(\u00123×π\u0013/7)");
assert_parsed_expression_simplify_to("cos(π×35/29)", "-cos(\u00126×π\u0013/29)");
assert_parsed_expression_simplify_to("cos(-π×35/29)", "-cos(\u00126×π\u0013/29)");
assert_parsed_expression_simplify_to("cos(π×340000)", "1");
assert_parsed_expression_simplify_to("cos(-π×340001)", "-1");
assert_parsed_expression_simplify_to("cos(-π×√(2))", "cos(√(2)π)");
assert_parsed_expression_simplify_to("cos(-π×√(2))", "cos(√(2)×π)");
assert_parsed_expression_simplify_to("cos(1311π/6)", "0");
assert_parsed_expression_simplify_to("cos(π/12)", "\u0012√(6)+√(2)\u0013/4");
assert_parsed_expression_simplify_to("cos(-π/12)", "\u0012√(6)+√(2)\u0013/4");
@@ -425,7 +425,7 @@ QUIZ_CASE(poincare_simplication_trigonometry_functions) {
assert_parsed_expression_simplify_to("cos(π/4+1000π)", "√(2)/2");
assert_parsed_expression_simplify_to("cos(-π/3)", "1/2");
assert_parsed_expression_simplify_to("cos(41π/5)", "\u0012√(5)+1\u0013/4");
assert_parsed_expression_simplify_to("cos(7π/10)", "-√(2)√(-√(5)+5)/4");
assert_parsed_expression_simplify_to("cos(7π/10)", "-\u0012√(2)×√(-√(5)+5)\u0013/4");
assert_parsed_expression_simplify_to("cos(0)", "1", User, Degree);
assert_parsed_expression_simplify_to("cos(180)", "-1", User, Degree);
assert_parsed_expression_simplify_to("cos(720/7)", "-cos(540/7)", User, Degree);
@@ -433,7 +433,7 @@ QUIZ_CASE(poincare_simplication_trigonometry_functions) {
assert_parsed_expression_simplify_to("cos(-6300/29)", "-cos(1080/29)", User, Degree);
assert_parsed_expression_simplify_to("cos(61200000)", "1", User, Degree);
assert_parsed_expression_simplify_to("cos(-61200180)", "-1", User, Degree);
assert_parsed_expression_simplify_to("cos(-180×√(2))", "cos(180√(2))", User, Degree);
assert_parsed_expression_simplify_to("cos(-180×√(2))", "cos(180×√(2))", User, Degree);
assert_parsed_expression_simplify_to("cos(39330)", "0", User, Degree);
assert_parsed_expression_simplify_to("cos(15)", "\u0012√(6)+√(2)\u0013/4", User, Degree);
assert_parsed_expression_simplify_to("cos(-15)", "\u0012√(6)+√(2)\u0013/4", User, Degree);
@@ -446,22 +446,22 @@ QUIZ_CASE(poincare_simplication_trigonometry_functions) {
// -- sin
assert_parsed_expression_simplify_to("sin(0)", "0");
assert_parsed_expression_simplify_to("sin(π)", "0");
assert_parsed_expression_simplify_to("sin(π×35/29)", "-sin(6π/29)");
assert_parsed_expression_simplify_to("sin(-π×35/29)", "sin(6π/29)");
assert_parsed_expression_simplify_to("sin(π×35/29)", "-sin(\u00126×π\u0013/29)");
assert_parsed_expression_simplify_to("sin(-π×35/29)", "sin(\u00126×π\u0013/29)");
assert_parsed_expression_simplify_to("sin(π×340000)", "0");
assert_parsed_expression_simplify_to("sin(π×340001)", "0");
assert_parsed_expression_simplify_to("sin(-π×340001)", "0");
assert_parsed_expression_simplify_to("sin(π/12)", "\u0012√(6)-√(2)\u0013/4");
assert_parsed_expression_simplify_to("sin(-π/12)", "\u0012-√(6)+√(2)\u0013/4");
assert_parsed_expression_simplify_to("sin(-π×√(2))", "-sin(√(2)π)");
assert_parsed_expression_simplify_to("sin(-π×√(2))", "-sin(√(2)×π)");
assert_parsed_expression_simplify_to("sin(1311π/6)", "1");
assert_parsed_expression_simplify_to("sin(-π17/8)", "-√(-√(2)+2)/2");
assert_parsed_expression_simplify_to("sin(41π/6)", "1/2");
assert_parsed_expression_simplify_to("sin(-3π/10)", "\u0012-√(5)-1\u0013/4");
assert_parsed_expression_simplify_to("sin(π/4+1000π)", "√(2)/2");
assert_parsed_expression_simplify_to("sin(-π/3)", "-√(3)/2");
assert_parsed_expression_simplify_to("sin(17π/5)", "-√(2)√(√(5)+5)/4");
assert_parsed_expression_simplify_to("sin(π/5)", "√(2)√(-√(5)+5)/4");
assert_parsed_expression_simplify_to("sin(17π/5)", "-\u0012√(2)×√(√(5)+5)\u0013/4");
assert_parsed_expression_simplify_to("sin(π/5)", "\u0012√(2)×√(-√(5)+5)\u0013/4");
assert_parsed_expression_simplify_to("sin(0)", "0", User, Degree);
assert_parsed_expression_simplify_to("sin(180)", "0", User, Degree);
assert_parsed_expression_simplify_to("sin(6300/29)", "-sin(1080/29)", User, Degree);
@@ -471,31 +471,31 @@ QUIZ_CASE(poincare_simplication_trigonometry_functions) {
assert_parsed_expression_simplify_to("sin(-61200180)", "0", User, Degree);
assert_parsed_expression_simplify_to("sin(15)", "\u0012√(6)-√(2)\u0013/4", User, Degree);
assert_parsed_expression_simplify_to("sin(-15)", "\u0012-√(6)+√(2)\u0013/4", User, Degree);
assert_parsed_expression_simplify_to("sin(-180×√(2))", "-sin(180√(2))", User, Degree);
assert_parsed_expression_simplify_to("sin(-180×√(2))", "-sin(180×√(2))", User, Degree);
assert_parsed_expression_simplify_to("sin(39330)", "1", User, Degree);
assert_parsed_expression_simplify_to("sin(-765/2)", "-√(-√(2)+2)/2", User, Degree);
assert_parsed_expression_simplify_to("sin(1230)", "1/2", User, Degree);
assert_parsed_expression_simplify_to("sin(180045)", "√(2)/2", User, Degree);
assert_parsed_expression_simplify_to("sin(-60)", "-√(3)/2", User, Degree);
assert_parsed_expression_simplify_to("sin(612)", "-√(2)√(√(5)+5)/4", User, Degree);
assert_parsed_expression_simplify_to("sin(36)", "√(2)√(-√(5)+5)/4", User, Degree);
assert_parsed_expression_simplify_to("sin(612)", "-\u0012√(2)×√(√(5)+5)\u0013/4", User, Degree);
assert_parsed_expression_simplify_to("sin(36)", "\u0012√(2)×√(-√(5)+5)\u0013/4", User, Degree);
// -- tan
assert_parsed_expression_simplify_to("tan(0)", "0");
assert_parsed_expression_simplify_to("tan(π)", "0");
assert_parsed_expression_simplify_to("tan(π×35/29)", "tan(6π/29)");
assert_parsed_expression_simplify_to("tan(-π×35/29)", "-tan(6π/29)");
assert_parsed_expression_simplify_to("tan(π×35/29)", "tan(\u00126×π\u0013/29)");
assert_parsed_expression_simplify_to("tan(-π×35/29)", "-tan(\u00126×π\u0013/29)");
assert_parsed_expression_simplify_to("tan(π×340000)", "0");
assert_parsed_expression_simplify_to("tan(π×340001)", "0");
assert_parsed_expression_simplify_to("tan(-π×340001)", "0");
assert_parsed_expression_simplify_to("tan(π/12)", "-√(3)+2");
assert_parsed_expression_simplify_to("tan(-π/12)", "√(3)-2");
assert_parsed_expression_simplify_to("tan(-π×√(2))", "-tan(√(2)π)");
assert_parsed_expression_simplify_to("tan(-π×√(2))", "-tan(√(2)×π)");
assert_parsed_expression_simplify_to("tan(1311π/6)", Undefined::Name());
assert_parsed_expression_simplify_to("tan(-π17/8)", "-√(2)+1");
assert_parsed_expression_simplify_to("tan(41π/6)", "-√(3)/3");
assert_parsed_expression_simplify_to("tan(π/4+1000π)", "1");
assert_parsed_expression_simplify_to("tan(-π/3)", "-√(3)");
assert_parsed_expression_simplify_to("tan(-π/10)", "-√(5)√(-2√(5)+5)/5");
assert_parsed_expression_simplify_to("tan(-π/10)", "-\u0012√(5)×√(-2×√(5)+5)\u0013/5");
assert_parsed_expression_simplify_to("tan(0)", "0", User, Degree);
assert_parsed_expression_simplify_to("tan(180)", "0", User, Degree);
assert_parsed_expression_simplify_to("tan(6300/29)", "tan(1080/29)", User, Degree);
@@ -505,7 +505,7 @@ QUIZ_CASE(poincare_simplication_trigonometry_functions) {
assert_parsed_expression_simplify_to("tan(-61200180)", "0", User, Degree);
assert_parsed_expression_simplify_to("tan(15)", "-√(3)+2", User, Degree);
assert_parsed_expression_simplify_to("tan(-15)", "√(3)-2", User, Degree);
assert_parsed_expression_simplify_to("tan(-180×√(2))", "-tan(180√(2))", User, Degree);
assert_parsed_expression_simplify_to("tan(-180×√(2))", "-tan(180×√(2))", User, Degree);
assert_parsed_expression_simplify_to("tan(39330)", Undefined::Name(), User, Degree);
assert_parsed_expression_simplify_to("tan(-382.5)", "-√(2)+1", User, Degree);
assert_parsed_expression_simplify_to("tan(1230)", "-√(3)/3", User, Degree);
@@ -513,14 +513,14 @@ QUIZ_CASE(poincare_simplication_trigonometry_functions) {
assert_parsed_expression_simplify_to("tan(-60)", "-√(3)", User, Degree);
assert_parsed_expression_simplify_to("tan(tan(tan(tan(9))))", "tan(tan(tan(tan(9))))");
// -- acos
assert_parsed_expression_simplify_to("acos(-1/2)", "2π/3");
assert_parsed_expression_simplify_to("acos(-1/2)", "\u00122×π\u0013/3");
assert_parsed_expression_simplify_to("acos(-1.2)", "-acos(6/5)+π");
assert_parsed_expression_simplify_to("acos(cos(2/3))", "2/3");
assert_parsed_expression_simplify_to("acos(cos(3/2))", "3/2");
assert_parsed_expression_simplify_to("cos(acos(3/2))", "3/2");
assert_parsed_expression_simplify_to("cos(acos(2/3))", "2/3");
assert_parsed_expression_simplify_to("acos(cos(12))", "acos(cos(12))");
assert_parsed_expression_simplify_to("acos(cos(4π/7))", "4π/7");
assert_parsed_expression_simplify_to("acos(cos(4π/7))", "\u00124×π\u0013/7");
assert_parsed_expression_simplify_to("acos(-cos(2))", "π-2");
assert_parsed_expression_simplify_to("acos(-1/2)", "120", User, Degree);
assert_parsed_expression_simplify_to("acos(-1.2)", "-acos(6/5)+180", User, Degree);
@@ -602,7 +602,7 @@ QUIZ_CASE(poincare_simplication_matrix) {
// Multiplication Matrix
assert_parsed_expression_simplify_to("2*[[1,2,3][4,5,6]]", "[[2,4,6][8,10,12]]");
assert_parsed_expression_simplify_to("[[1,2,3][4,5,6]]×√(2)", "[[√(2),2√(2),3√(2)][4√(2),5√(2),6√(2)]]");
assert_parsed_expression_simplify_to("[[1,2,3][4,5,6]]×√(2)", "[[√(2),2×√(2),3×√(2)][4×√(2),5×√(2),6×√(2)]]");
assert_parsed_expression_simplify_to("[[1,2][3,4]]*[[1,2,3][4,5,6]]", "[[9,12,15][19,26,33]]");
assert_parsed_expression_simplify_to("[[1,2,3][4,5,6]]*[[1,2][2,3][5,6]]", "[[20,26][44,59]]");
assert_parsed_expression_simplify_to("[[1,2,3,4][4,5,6,5]]*[[1,2][2,3][5,6]]", Undefined::Name());
@@ -615,15 +615,15 @@ QUIZ_CASE(poincare_simplication_matrix) {
assert_parsed_expression_simplify_to("[[1,2][3,4]]^(-1)", "[[-2,1][3/2,-1/2]]");
// Determinant
assert_parsed_expression_simplify_to("det(π+π)", "2π");
assert_parsed_expression_simplify_to("det([[π+π]])", "2π");
assert_parsed_expression_simplify_to("det(π+π)", "2×π");
assert_parsed_expression_simplify_to("det([[π+π]])", "2×π");
assert_parsed_expression_simplify_to("det([[1,2][3,4]])", "-2");
assert_parsed_expression_simplify_to("det([[2,2][3,4]])", "2");
assert_parsed_expression_simplify_to("det([[2,2][3,4][3,4]])", Undefined::Name());
assert_parsed_expression_simplify_to("det([[2,2][3,3]])", "0");
assert_parsed_expression_simplify_to("det([[1,2,3][4,5,6][7,8,9]])", "0");
assert_parsed_expression_simplify_to("det([[1,2,3][4,5,6][7,8,9]])", "0");
assert_parsed_expression_simplify_to("det([[1,2,3][4π,5,6][7,8,9]])", "24π-24");
assert_parsed_expression_simplify_to("det([[1,2,3][4π,5,6][7,8,9]])", "24×π-24");
// Dimension
assert_parsed_expression_simplify_to("dim(3)", "[[1,1]]");
@@ -632,7 +632,7 @@ QUIZ_CASE(poincare_simplication_matrix) {
// Inverse
assert_parsed_expression_simplify_to("inverse([[1/√(2),1/2,3][2,1,-3]])", Undefined::Name());
assert_parsed_expression_simplify_to("inverse([[1,2][3,4]])", "[[-2,1][3/2,-1/2]]");
assert_parsed_expression_simplify_to("inverse([[π,2π][3,2]])", "[[-1/2π,1/2][3/4π,-1/4]]");
assert_parsed_expression_simplify_to("inverse([[π,2×π][3,2]])", "[[-1/\u00122×π\u0013,1/2][3/\u00124×π\u0013,-1/4]]");
// Trace
assert_parsed_expression_simplify_to("trace([[1/√(2),1/2,3][2,1,-3]])", Undefined::Name());
@@ -712,7 +712,7 @@ QUIZ_CASE(poincare_simplification_functions_of_matrices) {
assert_parsed_expression_simplify_to("prediction(5,[[2,3]])", Undefined::Name());
assert_parsed_expression_simplify_to("prediction95([[2,3]],5)", Undefined::Name());
assert_parsed_expression_simplify_to("prediction95(5,[[2,3]])", Undefined::Name());
assert_parsed_expression_simplify_to("prediction95(1/3, 25)", "[[\u0012-49√(2)+125\u0013/375,\u001249√(2)+125\u0013/375]]");
assert_parsed_expression_simplify_to("prediction95(1/3, 25)", "[[\u0012-49×√(2)+125\u0013/375,\u001249×√(2)+125\u0013/375]]");
assert_parsed_expression_simplify_to("prediction95(45, 25)", Undefined::Name());
assert_parsed_expression_simplify_to("prediction95(1/3, -34)", Undefined::Name());
assert_parsed_expression_simplify_to("product(1,x,[[0,180]],1)", Undefined::Name());
@@ -787,20 +787,20 @@ QUIZ_CASE(poincare_simplification_complex_format) {
assert_parsed_expression_simplify_to("3", "3", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("inf", "inf", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("1+2+𝐢", "3+𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("-(5+2×𝐢)", "-5-2𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("(5+2×𝐢)", "5+2𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("𝐢+𝐢", "2𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("-2+2×𝐢", "-2+2𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("(3+𝐢)-(2+4×𝐢)", "1-3𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("(2+3×𝐢)×(4-2×𝐢)", "14+8𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("(3+𝐢)/2", "3/2+\u00121/2\u0013𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("(3+𝐢)/(2+𝐢)", "7/5-\u00121/5\u0013𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("-(5+2×𝐢)", "-5-2×𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("(5+2×𝐢)", "5+2×𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("𝐢+𝐢", "2×𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("-2+2×𝐢", "-2+2×𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("(3+𝐢)-(2+4×𝐢)", "1-3×𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("(2+3×𝐢)×(4-2×𝐢)", "14+8×𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("(3+𝐢)/2", "3/2+1/2×𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("(3+𝐢)/(2+𝐢)", "7/5-1/5×𝐢", User, Radian, Cartesian);
// The simplification of (3+𝐢)^(2+𝐢) in a Cartesian complex form generates to many nodes
//assert_parsed_expression_simplify_to("(3+𝐢)^(2+𝐢)", "10×cos((-4×atan(3)+ln(2)+ln(5)+2×π)/2)×ℯ^((2×atan(3)-π)/2)+10×sin((-4×atan(3)+ln(2)+ln(5)+2×π)/2)×ℯ^((2×atan(3)-π)/2)𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("(3+𝐢)^(2+𝐢)", "(𝐢+3)^\u0012𝐢+2\u0013", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("√(1+6𝐢)", "√(2√(37)+2)/2+\u0012√(2√(37)-2)/2\u0013𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("(1+𝐢)^2", "2𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("2×𝐢", "2𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("√(1+6𝐢)", "√(2×√(37)+2)/2+√(2×√(37)-2)/2×𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("(1+𝐢)^2", "2×𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("2×𝐢", "2×𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("𝐢!", "𝐢!", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("3!", "6", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("x!", "x!", User, Radian, Cartesian);
@@ -818,7 +818,7 @@ QUIZ_CASE(poincare_simplification_complex_format) {
// TODO: confidence is not simplified yet
//assert_parsed_expression_simplify_to("confidence(-2,-3)", "confidence(-2)", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("conj(-2)", "-2", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("conj(-2+2×𝐢+𝐢)", "-2-3𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("conj(-2+2×𝐢+𝐢)", "-2-3×𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("cos(12)", "cos(12)", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("cos(12+𝐢)", "cos(12+𝐢)", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("diff(3×x, x, 3)", "diff(3×x,x,3)", User, Radian, Cartesian);
@@ -833,9 +833,9 @@ QUIZ_CASE(poincare_simplification_complex_format) {
// TODO: dim is not simplified yet
//assert_parsed_expression_simplify_to("dim(x)", "dim(x)", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("root(2,𝐢)", "cos(ln(2))-sin(ln(2))𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("root(2,𝐢+1)", "√(2)×cos(\u001290×ln(2)\u0013/π)-√(2)×sin(\u001290×ln(2)\u0013/π)𝐢", User, Degree, Cartesian);
assert_parsed_expression_simplify_to("root(2,𝐢+1)", "√(2)×cos(ln(2)/2)-√(2)×sin(ln(2)/2)𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("root(2,𝐢)", "cos(ln(2))-sin(ln(2))×𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("root(2,𝐢+1)", "√(2)×cos(\u001290×ln(2)\u0013/π)-√(2)×sin(\u001290×ln(2)\u0013/π)×𝐢", User, Degree, Cartesian);
assert_parsed_expression_simplify_to("root(2,𝐢+1)", "√(2)×cos(ln(2)/2)-√(2)×sin(ln(2)/2)×𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("permute(10, 4)", "5040", User, Radian, Cartesian);
// TODO: prediction is not simplified yet
//assert_parsed_expression_simplify_to("prediction(-2,-3)", "prediction(-2)", User, Radian, Cartesian);
@@ -846,7 +846,7 @@ QUIZ_CASE(poincare_simplification_complex_format) {
assert_parsed_expression_simplify_to("sign(x)", "sign(x)", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("sin(23)", "sin(23)", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("sin(23+𝐢)", "sin(23+𝐢)", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("√(1-𝐢)", "√(2√(2)+2)/2-\u0012√(2√(2)-2)/2\u0013𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("√(1-𝐢)", "√(2×√(2)+2)/2-√(2×√(2)-2)/2×𝐢", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("tan(23)", "tan(23)", User, Radian, Cartesian);
assert_parsed_expression_simplify_to("tan(23+𝐢)", "tan(23+𝐢)", User, Radian, Cartesian);
@@ -866,49 +866,49 @@ QUIZ_CASE(poincare_simplification_complex_format) {
Ion::Storage::sharedStorage()->recordNamed("f.func").destroy();
// Polar
assert_parsed_expression_simplify_to("-2.3ᴇ3", "2300ℯ^\u0012π𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("-2.3ᴇ3", "2300×ℯ^\u0012π×𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("3", "3", User, Radian, Polar);
assert_parsed_expression_simplify_to("inf", "inf", User, Radian, Polar);
assert_parsed_expression_simplify_to("1+2+𝐢", "√(10)ℯ^\u0012\u0012\u0012-2×atan(3)+π\u0013/2\u0013𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("1+2+𝐢", "√(10)ℯ^\u0012\u0012\u0012-π×atan(3)+90π\u0013/180\u0013𝐢\u0013", User, Degree, Polar);
assert_parsed_expression_simplify_to("-(5+2×𝐢)", "√(29)ℯ^\u0012\u0012\u0012-2×atan(5/2)-π\u0013/2\u0013𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("(5+2×𝐢)", "√(29)ℯ^\u0012\u0012\u0012-2×atan(5/2)+π\u0013/2\u0013𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("𝐢+𝐢", "2ℯ^\u0012\u0012π/2\u0013𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("𝐢+𝐢", "2ℯ^\u0012\u0012π/2\u0013𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("-2+2×𝐢", "2√(2)ℯ^\u0012\u00123π/4\u0013𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("(3+𝐢)-(2+4×𝐢)", "√(10)ℯ^\u0012\u0012\u00122×atan(1/3)-π\u0013/2\u0013𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("(2+3×𝐢)×(4-2×𝐢)", "2√(65)ℯ^\u0012\u0012\u0012-2×atan(7/4)+π\u0013/2\u0013𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("(3+𝐢)/2", "\u0012√(10)/2\u0013ℯ^\u0012\u0012\u0012-2×atan(3)+π\u0013/2\u0013𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("(3+𝐢)/(2+𝐢)", "√(2)ℯ^\u0012\u0012\u00122×atan(7)-π\u0013/2\u0013𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("1+2+𝐢", "√(10)×ℯ^\u0012\u0012-2×atan(3)+π\u0013/2×𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("1+2+𝐢", "√(10)×ℯ^\u0012\u0012-π×atan(3)+90×π\u0013/180×𝐢\u0013", User, Degree, Polar);
assert_parsed_expression_simplify_to("-(5+2×𝐢)", "√(29)×ℯ^\u0012\u0012-2×atan(5/2)-π\u0013/2×𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("(5+2×𝐢)", "√(29)×ℯ^\u0012\u0012-2×atan(5/2)+π\u0013/2×𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("𝐢+𝐢", "2×ℯ^\u0012π/2×𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("𝐢+𝐢", "2×ℯ^\u0012π/2×𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("-2+2×𝐢", "2×√(2)×ℯ^\u0012\u00123×π\u0013/4×𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("(3+𝐢)-(2+4×𝐢)", "√(10)×ℯ^\u0012\u00122×atan(1/3)-π\u0013/2×𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("(2+3×𝐢)×(4-2×𝐢)", "2×√(65)×ℯ^\u0012\u0012-2×atan(7/4)+π\u0013/2×𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("(3+𝐢)/2", "√(10)/2×ℯ^\u0012\u0012-2×atan(3)+π\u0013/2×𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("(3+𝐢)/(2+𝐢)", "√(2)×ℯ^\u0012\u00122×atan(7)-π\u0013/2×𝐢\u0013", User, Radian, Polar);
// TODO: simplify atan(tan(x)) = x±k×pi?
//assert_parsed_expression_simplify_to("(3+𝐢)^(2+𝐢)", "10ℯ^\u0012\u00122×atan(3)-π\u0013/2\u0013×ℯ^\u0012\u0012\u0012-4×atan(3)+ln(2)+ln(5)+2π\u0013/2\u0013𝐢\u0013", User, Radian, Polar);
// The simplification of (3+𝐢)^(2+𝐢) in a Polar complex form generates to many nodes
//assert_parsed_expression_simplify_to("(3+𝐢)^(2+𝐢)", "10ℯ^\u0012\u00122×atan(3)-π\u0013/2\u0013×ℯ^\u0012\u0012atan(tan((-4×atan(3)+ln(2)+ln(5)+2×π)/2))+π\u0013𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("(3+𝐢)^(2+𝐢)", "(𝐢+3)^\u0012𝐢+2\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("(1+𝐢)^2", "2ℯ^\u0012\u0012π/2\u0013𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("2×𝐢", "2ℯ^\u0012\u0012π/2\u0013𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("(1+𝐢)^2", "2×ℯ^\u0012π/2×𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("2×𝐢", "2×ℯ^\u0012π/2×𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("3!", "6", User, Radian, Polar);
assert_parsed_expression_simplify_to("x!", "x!", User, Radian, Polar);
assert_parsed_expression_simplify_to("ℯ", "ℯ", User, Radian, Polar);
assert_parsed_expression_simplify_to("π", "π", User, Radian, Polar);
assert_parsed_expression_simplify_to("𝐢", "ℯ^\u0012\u0012π/2\u0013𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("𝐢", "ℯ^\u0012π/2×𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("abs(-3)", "3", User, Radian, Polar);
assert_parsed_expression_simplify_to("abs(-3+𝐢)", "√(10)", User, Radian, Polar);
assert_parsed_expression_simplify_to("conj(2×ℯ^(𝐢×π/2))", "2ℯ^\u0012-\u0012π/2\u0013𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("-2×ℯ^(𝐢×π/2)", "2ℯ^\u0012-\u0012π/2\u0013𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("conj(2×ℯ^(𝐢×π/2))", "2×ℯ^\u0012-π/2×𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("-2×ℯ^(𝐢×π/2)", "2×ℯ^\u0012-π/2×𝐢\u0013", User, Radian, Polar);
// User defined variable
assert_parsed_expression_simplify_to("a", "a", User, Radian, Polar);
// a = 2 + 𝐢
assert_simplify("2+𝐢→a", Radian, Polar);
assert_parsed_expression_simplify_to("a", "√(5)ℯ^\u0012\u0012\u0012-2×atan(2)+π\u0013/2\u0013𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("a", "√(5)×ℯ^\u0012\u0012-2×atan(2)+π\u0013/2×𝐢\u0013", User, Radian, Polar);
// Clean the storage for other tests
Ion::Storage::sharedStorage()->recordNamed("a.exp").destroy();
// User defined function
assert_parsed_expression_simplify_to("f(3)", "f(3)", User, Radian, Polar);
// f: x → x+1
assert_simplify("x+1+𝐢→f(x)", Radian, Polar);
assert_parsed_expression_simplify_to("f(3)", "√(17)ℯ^\u0012\u0012\u0012-2×atan(4)+π\u0013/2\u0013𝐢\u0013", User, Radian, Polar);
assert_parsed_expression_simplify_to("f(3)", "√(17)×ℯ^\u0012\u0012-2×atan(4)+π\u0013/2×𝐢\u0013", User, Radian, Polar);
// Clean the storage for other tests
Ion::Storage::sharedStorage()->recordNamed("f.func").destroy();
}
@@ -918,7 +918,7 @@ QUIZ_CASE(poincare_simplification_reduction_target) {
assert_parsed_expression_simplify_to("1/π+1/x", "\u0012x+π\u0013/\u0012π×x\u0013", User);
assert_parsed_expression_simplify_to("1/(1+𝐢)", "1/\u0012𝐢+1\u0013", System);
assert_parsed_expression_simplify_to("1/(1+𝐢)", "1/2-\u00121/2\u0013𝐢", User);
assert_parsed_expression_simplify_to("1/(1+𝐢)", "1/2-1/2×𝐢", User);
assert_parsed_expression_simplify_to("sin(x)/(cos(x)×cos(x))", "sin(x)/cos(x)^2", System);
assert_parsed_expression_simplify_to("sin(x)/(cos(x)×cos(x))", "tan(x)/cos(x)", User);
@@ -959,7 +959,7 @@ QUIZ_CASE(poincare_simplification_mix) {
// Common operation mix
assert_parsed_expression_simplify_to("(√(2)×π + √(2)×ℯ)/√(2)", "ℯ+π");
assert_parsed_expression_simplify_to("π+(3√(2)-2√(3))/25", "\u001225π-2√(3)+3√(2)\u0013/25");
assert_parsed_expression_simplify_to("π+(3√(2)-2√(3))/25", "\u001225×π-2×√(3)+3×√(2)\u0013/25");
assert_parsed_expression_simplify_to("ln(2+3)", "ln(5)");
assert_parsed_expression_simplify_to("3×A×B×C+4×cos(2)-2×A×B×C+A×B×C+ln(3)+4×A×B-5×A×B×C+cos(3)×ln(5)+cos(2)-45×cos(2)", "cos(3)×ln(5)+ln(3)-40×cos(2)+4×A×B-3×A×B×C");
assert_parsed_expression_simplify_to("2×A+3×cos(2)+3+4×ln(5)+5×A+2×ln(5)+1+0", "6×ln(5)+3×cos(2)+7×A+4");
@@ -970,24 +970,24 @@ QUIZ_CASE(poincare_simplification_mix) {
assert_parsed_expression_simplify_to("A^2^2×A+4×A^3", "A^5+4×A^3");
assert_parsed_expression_simplify_to("0.5+4×A×B-2.3+2×A×B-2×B×A^C-cos(4)+2×A^C×B+A×B×C×D", "\u0012-5×cos(4)+30×A×B+5×A×B×C×D-9\u0013/5");
assert_parsed_expression_simplify_to("(1+√(2))/5", "\u0012√(2)+1\u0013/5");
assert_parsed_expression_simplify_to("(2+√(6))^2", "4√(6)+10");
assert_parsed_expression_simplify_to("(2+√(6))^2", "4×√(6)+10");
assert_parsed_expression_simplify_to("tan(3)ln(2)+π", "tan(3)×ln(2)+π");
// Complex
assert_parsed_expression_simplify_to("𝐢", "𝐢");
assert_parsed_expression_simplify_to("√(-33)", "√(33)𝐢");
assert_parsed_expression_simplify_to("𝐢^(3/5)", "√(2)√(-√(5)+5)/4+\u0012\u0012√(5)+1\u0013/4\u0013𝐢");
assert_parsed_expression_simplify_to("√(-33)", "√(33)×𝐢");
assert_parsed_expression_simplify_to("𝐢^(3/5)", "\u0012√(2)×√(-√(5)+5)\u0013/4+\u0012√(5)+1\u0013/4×𝐢");
assert_parsed_expression_simplify_to("𝐢𝐢𝐢𝐢", "1");
assert_parsed_expression_simplify_to("√(-𝐢)", "√(2)/2-\u0012√(2)/2\u0013𝐢");
assert_parsed_expression_simplify_to("√(-𝐢)", "√(2)/2-√(2)/2×𝐢");
assert_parsed_expression_simplify_to("A×cos(9)𝐢𝐢ln(2)", "-A×cos(9)×ln(2)");
assert_parsed_expression_simplify_to("(√(2)+√(2)×𝐢)/2(√(2)+√(2)×𝐢)/2(√(2)+√(2)×𝐢)/2", "√(2)/32-\u0012√(2)/32\u0013𝐢");
assert_parsed_expression_simplify_to("(√(2)+√(2)×𝐢)/2(√(2)+√(2)×𝐢)/2(√(2)+√(2)×𝐢)/2", "√(2)/32-√(2)/32×𝐢");
assert_parsed_expression_simplify_to("root(5^((-𝐢)3^9),𝐢)", "1/ℯ^atan(tan(19683×ln(5)))");
assert_parsed_expression_simplify_to("𝐢^𝐢", "1/ℯ^\u0012π/2\u0013");
assert_parsed_expression_simplify_to("𝐢/(1+𝐢×√(x))", "𝐢/\u0012√(x)𝐢+1\u0013");
assert_parsed_expression_simplify_to("x+𝐢/(1+𝐢×√(x))", "\u0012\u0012x^\u00123/2\u0013\u0013𝐢+𝐢+x\u0013/\u0012√(x)𝐢+1\u0013");
assert_parsed_expression_simplify_to("𝐢/(1+𝐢×√(x))", "𝐢/\u0012√(x)×𝐢+1\u0013");
assert_parsed_expression_simplify_to("x+𝐢/(1+𝐢×√(x))", "\u0012x^\u00123/2\u0013×𝐢+𝐢+x\u0013/\u0012√(x)×𝐢+1\u0013");
//assert_parsed_expression_simplify_to("log(cos(9)^ln(6), cos(9))", "ln(2)+ln(3)"); // TODO: for this to work, we must know the sign of cos(9)
//assert_parsed_expression_simplify_to("log(cos(9)^ln(6), 9)", "ln(6)×log(cos(9), 9)"); // TODO: for this to work, we must know the sign of cos(9)
assert_parsed_expression_simplify_to("(((√(6)-√(2))/4)/((√(6)+√(2))/4))+1", "-√(3)+3");
assert_parsed_expression_simplify_to("1/√(𝐢) × (√(2)-𝐢×√(2))", "-2𝐢"); // TODO: get rid of complex at denominator?
assert_parsed_expression_simplify_to("1/√(𝐢) × (√(2)-𝐢×√(2))", "-2×𝐢"); // TODO: get rid of complex at denominator?
}